LMFDB - Embedded newform 670.2.k.c.461.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [670,2,Mod(81,670)]

mf = mfinit([N,k,chi],0)

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(670, base_ring=CyclotomicField(22))

chi = DirichletCharacter(H, H._module([0, 8]))

N = Newforms(chi, 2, names="a")

//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code

chi := DirichletCharacter("670.81");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 670 = 2 \cdot 5 \cdot 67 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	670.k (of order $11$, degree $10$, minimal)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

gp: f = lf[1] \\ Warning: the index may be different

Self dual:	no
Analytic conductor:	$5.34997693543$
Analytic rank:	$0$
Dimension:	$50$
Relative dimension:	$5$ over $\Q(\zeta_{11})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{11}]$

Embedding invariants

Embedding label			461.3
Character	$\chi$	$=$	670.461
Dual form			670.2.k.c.561.3

$q$-expansion

comment: q-expansion

sage: f.q_expansion() # note that sage often uses an isomorphic number field

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.142315 - 0.989821i) q^{2} +(-0.333595 - 0.384990i) q^{3} +(-0.959493 - 0.281733i) q^{4} +(0.841254 + 0.540641i) q^{5} +(-0.428547 + 0.275410i) q^{6} +(-0.617362 + 4.29385i) q^{7} +(-0.415415 + 0.909632i) q^{8} +(0.390013 - 2.71260i) q^{9} +O(q^{10})$	\(q+(0.142315 - 0.989821i) q^{2} +(-0.333595 - 0.384990i) q^{3} +(-0.959493 - 0.281733i) q^{4} +(0.841254 + 0.540641i) q^{5} +(-0.428547 + 0.275410i) q^{6} +(-0.617362 + 4.29385i) q^{7} +(-0.415415 + 0.909632i) q^{8} +(0.390013 - 2.71260i) q^{9} +(0.654861 - 0.755750i) q^{10} +(-2.08595 - 1.34056i) q^{11} +(0.211618 + 0.463380i) q^{12} +(1.18253 + 2.58938i) q^{13} +(4.16228 + 1.22216i) q^{14} +(-0.0724972 - 0.504229i) q^{15} +(0.841254 + 0.540641i) q^{16} +(6.50898 - 1.91121i) q^{17} +(-2.62949 - 0.772087i) q^{18} +(0.629819 + 4.38049i) q^{19} +(-0.654861 - 0.755750i) q^{20} +(1.85904 - 1.19473i) q^{21} +(-1.62377 + 1.87394i) q^{22} +(4.17021 + 4.81268i) q^{23} +(0.488779 - 0.143519i) q^{24} +(0.415415 + 0.909632i) q^{25} +(2.73132 - 0.801987i) q^{26} +(-2.46007 + 1.58099i) q^{27} +(1.80207 - 3.94598i) q^{28} +8.42041 q^{29} -0.509414 q^{30} +(-1.60564 + 3.51587i) q^{31} +(0.654861 - 0.755750i) q^{32} +(0.179762 + 1.25027i) q^{33} +(-0.965431 - 6.71472i) q^{34} +(-2.84079 + 3.27844i) q^{35} +(-1.13844 + 2.49284i) q^{36} -4.35537 q^{37} +4.42554 q^{38} +(0.602398 - 1.31907i) q^{39} +(-0.841254 + 0.540641i) q^{40} +(-1.51640 + 0.445257i) q^{41} +(-0.918001 - 2.01014i) q^{42} +(10.7484 - 3.15600i) q^{43} +(1.62377 + 1.87394i) q^{44} +(1.79464 - 2.07113i) q^{45} +(5.35718 - 3.44285i) q^{46} +(-2.92349 - 3.37388i) q^{47} +(-0.0724972 - 0.504229i) q^{48} +(-11.3395 - 3.32959i) q^{49} +(0.959493 - 0.281733i) q^{50} +(-2.90716 - 1.86832i) q^{51} +(-0.405117 - 2.81765i) q^{52} +(1.24234 + 0.364785i) q^{53} +(1.21479 + 2.66003i) q^{54} +(-1.03005 - 2.25550i) q^{55} +(-3.64936 - 2.34530i) q^{56} +(1.47634 - 1.70379i) q^{57} +(1.19835 - 8.33470i) q^{58} +(1.08440 - 2.37451i) q^{59} +(-0.0724972 + 0.504229i) q^{60} +(-1.28175 + 0.823733i) q^{61} +(3.25157 + 2.08966i) q^{62} +(11.4067 + 3.34932i) q^{63} +(-0.654861 - 0.755750i) q^{64} +(-0.405117 + 2.81765i) q^{65} +1.26313 q^{66} +(-3.40210 - 7.44484i) q^{67} -6.78377 q^{68} +(0.461669 - 3.21098i) q^{69} +(2.84079 + 3.27844i) q^{70} +(-8.50817 - 2.49822i) q^{71} +(2.30545 + 1.48162i) q^{72} +(4.76950 - 3.06517i) q^{73} +(-0.619834 + 4.31104i) q^{74} +(0.211618 - 0.463380i) q^{75} +(0.629819 - 4.38049i) q^{76} +(7.04394 - 8.12913i) q^{77} +(-1.21991 - 0.783989i) q^{78} +(6.84700 + 14.9928i) q^{79} +(0.415415 + 0.909632i) q^{80} +(-6.45913 - 1.89657i) q^{81} +(0.224918 + 1.56434i) q^{82} +(1.66059 + 1.06720i) q^{83} +(-2.12033 + 0.622584i) q^{84} +(6.50898 + 1.91121i) q^{85} +(-1.59423 - 11.0881i) q^{86} +(-2.80901 - 3.24177i) q^{87} +(2.08595 - 1.34056i) q^{88} +(-11.0148 + 12.7118i) q^{89} +(-1.79464 - 2.07113i) q^{90} +(-11.8485 + 3.47902i) q^{91} +(-2.64540 - 5.79262i) q^{92} +(1.88921 - 0.554721i) q^{93} +(-3.75560 + 2.41358i) q^{94} +(-1.83843 + 4.02561i) q^{95} -0.509414 q^{96} -15.0408 q^{97} +(-4.90948 + 10.7503i) q^{98} +(-4.44995 + 5.13552i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 50 q + 5 q^{2} - 2 q^{3} - 5 q^{4} - 5 q^{5} + 2 q^{6} - q^{7} + 5 q^{8} - q^{9}+O(q^{10}) $ 50 * q + 5 * q^2 - 2 * q^3 - 5 * q^4 - 5 * q^5 + 2 * q^6 - q^7 + 5 * q^8 - q^9	\( 50 q + 5 q^{2} - 2 q^{3} - 5 q^{4} - 5 q^{5} + 2 q^{6} - q^{7} + 5 q^{8} - q^{9} + 5 q^{10} - 12 q^{11} - 2 q^{12} + 24 q^{13} + 23 q^{14} - 2 q^{15} - 5 q^{16} + 31 q^{17} + q^{18} + 4 q^{19} - 5 q^{20} + 12 q^{21} + q^{22} + 27 q^{23} - 9 q^{24} - 5 q^{25} - 2 q^{26} - 14 q^{27} + 10 q^{28} - 36 q^{29} + 2 q^{30} - 13 q^{31} + 5 q^{32} - 42 q^{33} + 2 q^{34} + 21 q^{35} - q^{36} - 50 q^{37} - 26 q^{38} - 31 q^{39} + 5 q^{40} - 10 q^{41} + 21 q^{42} + 16 q^{43} - q^{44} - q^{45} + 17 q^{46} - 13 q^{47} - 2 q^{48} - 40 q^{49} + 5 q^{50} - 19 q^{51} - 20 q^{52} - 5 q^{53} + 47 q^{54} + 10 q^{55} + 12 q^{56} - 90 q^{57} - 8 q^{58} - 20 q^{59} - 2 q^{60} + 12 q^{61} + 13 q^{62} - 15 q^{63} - 5 q^{64} - 20 q^{65} + 20 q^{66} - 21 q^{67} - 24 q^{68} + 77 q^{69} - 21 q^{70} + 24 q^{71} + 12 q^{72} - 68 q^{73} - 16 q^{74} - 2 q^{75} + 4 q^{76} + 7 q^{77} + 53 q^{78} - 26 q^{79} - 5 q^{80} - 21 q^{81} + 21 q^{82} - 10 q^{83} + 12 q^{84} + 31 q^{85} - 27 q^{86} + 61 q^{87} + 12 q^{88} + 51 q^{89} + q^{90} - 10 q^{91} - 6 q^{92} - 38 q^{93} - 9 q^{94} + 15 q^{95} + 2 q^{96} + 72 q^{97} - 37 q^{98} - 32 q^{99}+O(q^{100}) \) 50 * q + 5 * q^2 - 2 * q^3 - 5 * q^4 - 5 * q^5 + 2 * q^6 - q^7 + 5 * q^8 - q^9 + 5 * q^10 - 12 * q^11 - 2 * q^12 + 24 * q^13 + 23 * q^14 - 2 * q^15 - 5 * q^16 + 31 * q^17 + q^18 + 4 * q^19 - 5 * q^20 + 12 * q^21 + q^22 + 27 * q^23 - 9 * q^24 - 5 * q^25 - 2 * q^26 - 14 * q^27 + 10 * q^28 - 36 * q^29 + 2 * q^30 - 13 * q^31 + 5 * q^32 - 42 * q^33 + 2 * q^34 + 21 * q^35 - q^36 - 50 * q^37 - 26 * q^38 - 31 * q^39 + 5 * q^40 - 10 * q^41 + 21 * q^42 + 16 * q^43 - q^44 - q^45 + 17 * q^46 - 13 * q^47 - 2 * q^48 - 40 * q^49 + 5 * q^50 - 19 * q^51 - 20 * q^52 - 5 * q^53 + 47 * q^54 + 10 * q^55 + 12 * q^56 - 90 * q^57 - 8 * q^58 - 20 * q^59 - 2 * q^60 + 12 * q^61 + 13 * q^62 - 15 * q^63 - 5 * q^64 - 20 * q^65 + 20 * q^66 - 21 * q^67 - 24 * q^68 + 77 * q^69 - 21 * q^70 + 24 * q^71 + 12 * q^72 - 68 * q^73 - 16 * q^74 - 2 * q^75 + 4 * q^76 + 7 * q^77 + 53 * q^78 - 26 * q^79 - 5 * q^80 - 21 * q^81 + 21 * q^82 - 10 * q^83 + 12 * q^84 + 31 * q^85 - 27 * q^86 + 61 * q^87 + 12 * q^88 + 51 * q^89 + q^90 - 10 * q^91 - 6 * q^92 - 38 * q^93 - 9 * q^94 + 15 * q^95 + 2 * q^96 + 72 * q^97 - 37 * q^98 - 32 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/670\mathbb{Z}\right)^\times$.

$n$	$471$	$537$
$\chi(n)$	$e\left(\frac{6}{11}\right)$	$1$

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$			$a_n / n^{(k-1)/2}$			$ \alpha_n $			$ \theta_n $
$p$	$a_p$			$a_p / p^{(k-1)/2}$			$ \alpha_p$			$ \theta_p $

$2$	0.142315	−	0.989821i	0.100632	−	0.699909i
$2$	0.142315	−	0.989821i	0.100632	−	0.699909i
$3$	−0.333595	−	0.384990i	−0.192601	−	0.222274i	0.651233	−	0.758878i	$-0.274252\pi$
$3$	−0.333595	−	0.384990i	−0.192601	−	0.222274i	−0.843834	+	0.536604i	$0.819707\pi$
$4$	−0.959493	−	0.281733i	−0.479746	−	0.140866i
$5$	0.841254	+	0.540641i	0.376220	+	0.241782i
$5$	0.841254	+	0.540641i	0.376220	+	0.241782i
$6$	−0.428547	+	0.275410i	−0.174953	+	0.112436i
$7$	−0.617362	+	4.29385i	−0.233341	+	1.62292i	0.450144	+	0.892956i	$0.351373\pi$
$7$	−0.617362	+	4.29385i	−0.233341	+	1.62292i	−0.683484	+	0.729965i	$0.739536\pi$
$8$	−0.415415	+	0.909632i	−0.146871	+	0.321603i
$9$	0.390013	−	2.71260i	0.130004	−	0.904201i
$10$	0.654861	−	0.755750i	0.207085	−	0.238989i
$11$	−2.08595	−	1.34056i	−0.628937	−	0.404193i	0.186979	−	0.982364i	$-0.440130\pi$
$11$	−2.08595	−	1.34056i	−0.628937	−	0.404193i	−0.815916	+	0.578171i	$0.803767\pi$
$12$	0.211618	+	0.463380i	0.0610890	+	0.133766i
$13$	1.18253	+	2.58938i	0.327975	+	0.718165i	0.999745	−	0.0225950i	$-0.00719281\pi$
$13$	1.18253	+	2.58938i	0.327975	+	0.718165i	−0.671770	+	0.740760i	$0.734466\pi$
$14$	4.16228	+	1.22216i	1.11242	+	0.326635i
$15$	−0.0724972	−	0.504229i	−0.0187187	−	0.130191i
$16$	0.841254	+	0.540641i	0.210313	+	0.135160i
$17$	6.50898	−	1.91121i	1.57866	−	0.463536i	0.629152	−	0.777282i	$-0.283402\pi$
$17$	6.50898	−	1.91121i	1.57866	−	0.463536i	0.949507	+	0.313746i	$0.101584\pi$
$18$	−2.62949	−	0.772087i	−0.619776	−	0.181983i
$19$	0.629819	+	4.38049i	0.144490	+	1.00495i	0.925043	+	0.379863i	$0.124029\pi$
$19$	0.629819	+	4.38049i	0.144490	+	1.00495i	−0.780552	+	0.625090i	$0.785062\pi$
$20$	−0.654861	−	0.755750i	−0.146431	−	0.168991i
$21$	1.85904	−	1.19473i	0.405675	−	0.260711i
$22$	−1.62377	+	1.87394i	−0.346190	+	0.399524i
$23$	4.17021	+	4.81268i	0.869549	+	1.00351i	0.999927	+	0.0120491i	$0.00383545\pi$
$23$	4.17021	+	4.81268i	0.869549	+	1.00351i	−0.130378	+	0.991464i	$0.541619\pi$
$24$	0.488779	−	0.143519i	0.0997717	−	0.0292956i
$25$	0.415415	+	0.909632i	0.0830830	+	0.181926i
$26$	2.73132	−	0.801987i	0.535655	−	0.157283i
$27$	−2.46007	+	1.58099i	−0.473441	+	0.304262i
$28$	1.80207	−	3.94598i	0.340559	−	0.745721i
$29$	8.42041			1.56363			0.781815	−	0.623510i	$-0.214294\pi$
$29$	8.42041			1.56363			0.781815	+	0.623510i	$0.214294\pi$
$30$	−0.509414			−0.0930059
$31$	−1.60564	+	3.51587i	−0.288382	+	0.631468i	−0.997269	−	0.0738536i	$-0.976470\pi$
$31$	−1.60564	+	3.51587i	−0.288382	+	0.631468i	0.708887	+	0.705322i	$0.249198\pi$
$32$	0.654861	−	0.755750i	0.115764	−	0.133599i
$33$	0.179762	+	1.25027i	0.0312926	+	0.217645i
$34$	−0.965431	−	6.71472i	−0.165570	−	1.15156i
$35$	−2.84079	+	3.27844i	−0.480181	+	0.554158i
$36$	−1.13844	+	2.49284i	−0.189741	+	0.415474i
$37$	−4.35537			−0.716019			−0.358010	−	0.933718i	$-0.616544\pi$
$37$	−4.35537			−0.716019			−0.358010	+	0.933718i	$0.616544\pi$
$38$	4.42554			0.717917
$39$	0.602398	−	1.31907i	0.0964609	−	0.211220i
$40$	−0.841254	+	0.540641i	−0.133014	+	0.0854828i
$41$	−1.51640	+	0.445257i	−0.236823	+	0.0695374i	−0.397990	−	0.917390i	$-0.630292\pi$
$41$	−1.51640	+	0.445257i	−0.236823	+	0.0695374i	0.161168	+	0.986927i	$0.448474\pi$
$42$	−0.918001	−	2.01014i	−0.141651	−	0.310171i
$43$	10.7484	−	3.15600i	1.63911	−	0.481286i	0.673048	−	0.739599i	$-0.264985\pi$
$43$	10.7484	−	3.15600i	1.63911	−	0.481286i	0.966061	+	0.258313i	$0.0831666\pi$
$44$	1.62377	+	1.87394i	0.244793	+	0.282506i
$45$	1.79464	−	2.07113i	0.267530	−	0.308746i
$46$	5.35718	−	3.44285i	0.789873	−	0.507620i
$47$	−2.92349	−	3.37388i	−0.426434	−	0.492132i	0.501352	−	0.865243i	$-0.332836\pi$
$47$	−2.92349	−	3.37388i	−0.426434	−	0.492132i	−0.927786	+	0.373112i	$0.878291\pi$
$48$	−0.0724972	−	0.504229i	−0.0104641	−	0.0727792i
$49$	−11.3395	−	3.32959i	−1.61993	−	0.475655i
$50$	0.959493	−	0.281733i	0.135693	−	0.0398430i
$51$	−2.90716	−	1.86832i	−0.407084	−	0.261617i
$52$	−0.405117	−	2.81765i	−0.0561796	−	0.390738i
$53$	1.24234	+	0.364785i	0.170649	+	0.0501071i	0.365941	−	0.930638i	$-0.380747\pi$
$53$	1.24234	+	0.364785i	0.170649	+	0.0501071i	−0.195292	+	0.980745i	$0.562565\pi$
$54$	1.21479	+	2.66003i	0.165313	+	0.361984i
$55$	−1.03005	−	2.25550i	−0.138892	−	0.304131i
$56$	−3.64936	−	2.34530i	−0.487666	−	0.313404i
$57$	1.47634	−	1.70379i	0.195546	−	0.225672i
$58$	1.19835	−	8.33470i	0.157351	−	1.09440i
$59$	1.08440	−	2.37451i	0.141177	−	0.309134i	−0.825815	−	0.563941i	$-0.809285\pi$
$59$	1.08440	−	2.37451i	0.141177	−	0.309134i	0.966992	+	0.254807i	$0.0820118\pi$
$60$	−0.0724972	+	0.504229i	−0.00935935	+	0.0650957i
$61$	−1.28175	+	0.823733i	−0.164112	+	0.105468i	−0.620119	−	0.784508i	$-0.712916\pi$
$61$	−1.28175	+	0.823733i	−0.164112	+	0.105468i	0.456007	+	0.889976i	$0.349279\pi$
$62$	3.25157	+	2.08966i	0.412950	+	0.265387i
$63$	11.4067	+	3.34932i	1.43711	+	0.421974i
$64$	−0.654861	−	0.755750i	−0.0818576	−	0.0944687i
$65$	−0.405117	+	2.81765i	−0.0502486	+	0.349487i
$66$	1.26313			0.155480
$67$	−3.40210	−	7.44484i	−0.415633	−	0.909532i
$67$	−3.40210	−	7.44484i	−0.415633	−	0.909532i
$68$	−6.78377			−0.822653
$69$	0.461669	−	3.21098i	0.0555784	−	0.386556i
$70$	2.84079	+	3.27844i	0.339539	+	0.391849i
$71$	−8.50817	−	2.49822i	−1.00973	−	0.296485i	−0.265289	−	0.964169i	$-0.585467\pi$
$71$	−8.50817	−	2.49822i	−1.00973	−	0.296485i	−0.744445	+	0.667684i	$0.767286\pi$
$72$	2.30545	+	1.48162i	0.271700	+	0.174611i
$73$	4.76950	−	3.06517i	0.558227	−	0.358751i	−0.230903	−	0.972977i	$-0.574168\pi$
$73$	4.76950	−	3.06517i	0.558227	−	0.358751i	0.789130	+	0.614226i	$0.210532\pi$
$74$	−0.619834	+	4.31104i	−0.0720543	+	0.501148i
$75$	0.211618	−	0.463380i	0.0244356	−	0.0535065i
$76$	0.629819	−	4.38049i	0.0722452	−	0.502477i
$77$	7.04394	−	8.12913i	0.802731	−	0.926401i
$78$	−1.21991	−	0.783989i	−0.138128	−	0.0887693i
$79$	6.84700	+	14.9928i	0.770347	+	1.68683i	0.725887	+	0.687814i	$0.241430\pi$
$79$	6.84700	+	14.9928i	0.770347	+	1.68683i	0.0444608	+	0.999011i	$0.485843\pi$
$80$	0.415415	+	0.909632i	0.0464448	+	0.101700i
$81$	−6.45913	−	1.89657i	−0.717681	−	0.210730i
$82$	0.224918	+	1.56434i	0.0248380	+	0.172752i
$83$	1.66059	+	1.06720i	0.182274	+	0.117140i	0.628596	−	0.777732i	$-0.283630\pi$
$83$	1.66059	+	1.06720i	0.182274	+	0.117140i	−0.446322	+	0.894872i	$0.647266\pi$
$84$	−2.12033	+	0.622584i	−0.231346	+	0.0679295i
$85$	6.50898	+	1.91121i	0.705998	+	0.207300i
$86$	−1.59423	−	11.0881i	−0.171910	−	1.19566i
$87$	−2.80901	−	3.24177i	−0.301158	−	0.347554i
$88$	2.08595	−	1.34056i	0.222363	−	0.142904i
$89$	−11.0148	+	12.7118i	−1.16757	+	1.34745i	−0.241363	+	0.970435i	$0.577594\pi$
$89$	−11.0148	+	12.7118i	−1.16757	+	1.34745i	−0.926208	+	0.377013i	$0.876951\pi$
$90$	−1.79464	−	2.07113i	−0.189172	−	0.218316i
$91$	−11.8485	+	3.47902i	−1.24206	+	0.364700i
$92$	−2.64540	−	5.79262i	−0.275802	−	0.603922i
$93$	1.88921	−	0.554721i	0.195902	−	0.0575219i
$94$	−3.75560	+	2.41358i	−0.387360	+	0.248941i
$95$	−1.83843	+	4.02561i	−0.188619	+	0.413019i
$96$	−0.509414			−0.0519919
$97$	−15.0408			−1.52716			−0.763582	−	0.645710i	$-0.776561\pi$
$97$	−15.0408			−1.52716			−0.763582	+	0.645710i	$0.776561\pi$
$98$	−4.90948	+	10.7503i	−0.495932	+	1.08594i
$99$	−4.44995	+	5.13552i	−0.447237	+	0.516139i
$100$	−0.142315	−	0.989821i	−0.0142315	−	0.0989821i
$101$	1.01382	+	7.05125i	0.100879	+	0.701626i	0.976008	+	0.217736i	$0.0698672\pi$
$101$	1.01382	+	7.05125i	0.100879	+	0.701626i	−0.875129	+	0.483889i	$0.839224\pi$
$102$	−2.26303	+	2.61168i	−0.224074	+	0.258595i
$103$	−2.36881	+	5.18698i	−0.233406	+	0.511088i	−0.989702	−	0.143141i	$-0.954280\pi$
$103$	−2.36881	+	5.18698i	−0.233406	+	0.511088i	0.756296	+	0.654229i	$0.227007\pi$
$104$	−2.84662			−0.279135
$105$	2.20984			0.215658
$106$	0.537876	−	1.17778i	0.0522432	−	0.114397i
$107$	1.87719	−	1.20640i	0.181475	−	0.116627i	−0.446749	−	0.894659i	$-0.647418\pi$
$107$	1.87719	−	1.20640i	0.181475	−	0.116627i	0.628224	+	0.778032i	$0.283782\pi$
$108$	2.80584	−	0.823868i	0.269992	−	0.0792767i
$109$	2.88499	+	6.31724i	0.276332	+	0.605082i	0.996012	−	0.0892242i	$-0.0284388\pi$
$109$	2.88499	+	6.31724i	0.276332	+	0.605082i	−0.719680	+	0.694306i	$0.755711\pi$
$110$	−2.37913	+	0.698576i	−0.226841	+	0.0666066i
$111$	1.45293	+	1.67677i	0.137906	+	0.159152i
$112$	−2.84079	+	3.27844i	−0.268429	+	0.309784i
$113$	15.1088	−	9.70985i	1.42132	−	0.913426i	0.421339	−	0.906903i	$-0.361560\pi$
$113$	15.1088	−	9.70985i	1.42132	−	0.913426i	0.999979	−	0.00652273i	$-0.00207626\pi$
$114$	−1.47634	−	1.70379i	−0.138272	−	0.159574i
$115$	0.906274	+	6.30327i	0.0845105	+	0.587783i
$116$	−8.07932	−	2.37230i	−0.750146	−	0.220263i
$117$	7.48517	−	2.19784i	0.692004	−	0.203191i
$118$	−2.19601	−	1.41129i	−0.202159	−	0.129920i
$119$	4.18804	+	29.1285i	0.383917	+	2.67020i
$120$	0.488779	+	0.143519i	0.0446193	+	0.0131014i
$121$	−2.01548	−	4.41328i	−0.183225	−	0.401207i
$122$	0.632936	+	1.38594i	0.0573033	+	0.125477i
$123$	0.677285	+	0.435264i	0.0610687	+	0.0392465i
$124$	2.53114	−	2.92109i	0.227303	−	0.262321i
$125$	−0.142315	+	0.989821i	−0.0127290	+	0.0885323i
$126$	4.93857	−	10.8140i	0.439963	−	0.963384i
$127$	1.08517	−	7.54751i	0.0962931	−	0.669733i	−0.883310	−	0.468790i	$-0.844690\pi$
$127$	1.08517	−	7.54751i	0.0962931	−	0.669733i	0.979603	−	0.200943i	$-0.0644007\pi$
$128$	−0.841254	+	0.540641i	−0.0743570	+	0.0477863i
$129$	−4.80063	−	3.08518i	−0.422672	−	0.271635i
$130$	2.73132	+	0.801987i	0.239552	+	0.0703389i
$131$	−7.42586	−	8.56990i	−0.648800	−	0.748755i	0.332105	−	0.943242i	$-0.392241\pi$
$131$	−7.42586	−	8.56990i	−0.648800	−	0.748755i	−0.980905	+	0.194487i	$0.937696\pi$
$132$	0.179762	−	1.25027i	0.0156463	−	0.108822i
$133$	−19.1980			−1.66468
$134$	−7.85324	+	2.30796i	−0.678416	+	0.199378i
$135$	−2.92429			−0.251683
$136$	−0.965431	+	6.71472i	−0.0827850	+	0.575782i
$137$	0.577504	+	0.666475i	0.0493395	+	0.0569408i	0.779883	−	0.625925i	$-0.215279\pi$
$137$	0.577504	+	0.666475i	0.0493395	+	0.0569408i	−0.730543	+	0.682866i	$0.760733\pi$
$138$	−3.11259	−	0.913939i	−0.264961	−	0.0777997i
$139$	−11.4412	−	7.35283i	−0.970432	−	0.623659i	−0.0435655	−	0.999051i	$-0.513872\pi$
$139$	−11.4412	−	7.35283i	−0.970432	−	0.623659i	−0.926866	+	0.375392i	$0.877508\pi$
$140$	3.64936	−	2.34530i	0.308427	−	0.198214i
$141$	−0.323648	+	2.25102i	−0.0272561	+	0.189570i
$142$	−3.68363	+	8.06603i	−0.309124	+	0.676886i
$143$	1.00452	−	6.98657i	0.0840019	−	0.584246i
$144$	1.79464	−	2.07113i	0.149554	−	0.172594i
$145$	7.08370	+	4.55242i	0.588269	+	0.378058i
$146$	−2.35520	−	5.15717i	−0.194918	−	0.426810i
$147$	2.50096	+	5.47634i	0.206276	+	0.451681i
$148$	4.17895	+	1.22705i	0.343508	+	0.100863i
$149$	−3.43832	−	23.9141i	−0.281678	−	1.95912i	−0.283009	−	0.959117i	$-0.591333\pi$
$149$	−3.43832	−	23.9141i	−0.281678	−	1.95912i	0.00133097	−	0.999999i	$-0.499576\pi$
$150$	−0.428547	−	0.275410i	−0.0349907	−	0.0224871i
$151$	11.6602	−	3.42373i	0.948891	−	0.278620i	0.229566	−	0.973293i	$-0.426269\pi$
$151$	11.6602	−	3.42373i	0.948891	−	0.278620i	0.719325	+	0.694674i	$0.244451\pi$
$152$	−4.24627	−	1.24682i	−0.344418	−	0.101130i
$153$	−2.64576	−	18.4017i	−0.213897	−	1.48769i
$154$	−7.04394	−	8.12913i	−0.567616	−	0.655064i
$155$	−3.25157	+	2.08966i	−0.261173	+	0.167845i
$156$	−0.949621	+	1.09592i	−0.0760305	+	0.0877439i
$157$	3.05207	+	3.52228i	0.243582	+	0.281108i	0.864355	−	0.502882i	$-0.167727\pi$
$157$	3.05207	+	3.52228i	0.243582	+	0.281108i	−0.620774	+	0.783990i	$0.713181\pi$
$158$	15.8147	−	4.64360i	1.25815	−	0.369425i
$159$	−0.274002	−	0.599980i	−0.0217298	−	0.0475815i
$160$	0.959493	−	0.281733i	0.0758546	−	0.0222729i
$161$	−23.2394	+	14.9351i	−1.83152	+	1.17705i
$162$	−2.79650	+	6.12347i	−0.219714	+	0.481106i
$163$	−1.32251			−0.103587			−0.0517935	−	0.998658i	$-0.516494\pi$
$163$	−1.32251			−0.103587			−0.0517935	+	0.998658i	$0.516494\pi$
$164$	1.58042			0.123410
$165$	−0.524723	+	1.14898i	−0.0408496	+	0.0894482i
$166$	1.29266	−	1.49181i	0.100330	−	0.115787i
$167$	1.92012	+	13.3547i	0.148583	+	1.03342i	0.918542	+	0.395324i	$0.129368\pi$
$167$	1.92012	+	13.3547i	0.148583	+	1.03342i	−0.769959	+	0.638094i	$0.779723\pi$
$168$	0.314493	+	2.18735i	0.0242637	+	0.168757i
$169$	3.20667	−	3.70070i	0.246667	−	0.284669i
$170$	2.81808	−	6.17073i	0.216137	−	0.473274i
$171$	12.1282			0.927464
$172$	−11.2021			−0.854154
$173$	−7.28332	+	15.9482i	−0.553741	+	1.21252i	0.401272	+	0.915959i	$0.368568\pi$
$173$	−7.28332	+	15.9482i	−0.553741	+	1.21252i	−0.955013	+	0.296564i	$0.904159\pi$
$174$	−3.60854	+	2.31907i	−0.273563	+	0.175808i
$175$	−4.16228	+	1.22216i	−0.314639	+	0.0923863i
$176$	−1.03005	−	2.25550i	−0.0776431	−	0.170015i
$177$	−1.27591	+	0.374641i	−0.0959034	+	0.0281598i
$178$	11.0148	+	12.7118i	0.825597	+	0.952790i
$179$	9.07152	−	10.4691i	0.678037	−	0.782497i	−0.307574	−	0.951524i	$-0.599517\pi$
$179$	9.07152	−	10.4691i	0.678037	−	0.782497i	0.985611	+	0.169027i	$0.0540626\pi$
$180$	−2.30545	+	1.48162i	−0.171838	+	0.110434i
$181$	−7.84337	−	9.05174i	−0.582993	−	0.672810i	0.385252	−	0.922811i	$-0.374114\pi$
$181$	−7.84337	−	9.05174i	−0.582993	−	0.672810i	−0.968246	+	0.250001i	$0.919569\pi$
$182$	1.75740	+	12.2230i	0.130267	+	0.906027i
$183$	0.744716	+	0.218668i	0.0550510	+	0.0161644i
$184$	−6.11014	+	1.79410i	−0.450445	+	0.132263i
$185$	−3.66397	−	2.35469i	−0.269381	−	0.173120i
$186$	−0.280213	−	1.94892i	−0.0205462	−	0.142902i
$187$	−16.1395	−	4.73898i	−1.18024	−	0.346548i
$188$	1.85453	+	4.06086i	0.135256	+	0.296169i
$189$	−5.26978	−	11.5392i	−0.383320	−	0.839354i
$190$	3.72300	+	2.39263i	0.270095	+	0.173579i
$191$	−0.889977	+	1.02709i	−0.0643965	+	0.0743175i	−0.787034	−	0.616910i	$-0.788384\pi$
$191$	−0.889977	+	1.02709i	−0.0643965	+	0.0743175i	0.722637	+	0.691227i	$0.242930\pi$
$192$	−0.0724972	+	0.504229i	−0.00523204	+	0.0363896i
$193$	−2.20817	+	4.83522i	−0.158947	+	0.348046i	−0.972304	−	0.233719i	$-0.924910\pi$
$193$	−2.20817	+	4.83522i	−0.158947	+	0.348046i	0.813357	+	0.581765i	$0.197638\pi$
$194$	−2.14053	+	14.8877i	−0.153681	+	1.06888i
$195$	1.21991	−	0.783989i	0.0873597	−	0.0561426i
$196$	9.94215	+	6.38943i	0.710153	+	0.456388i
$197$	10.3471	+	3.03818i	0.737199	+	0.216461i	0.628714	−	0.777637i	$-0.283582\pi$
$197$	10.3471	+	3.03818i	0.737199	+	0.216461i	0.108485	+	0.994098i	$0.465400\pi$
$198$	4.44995	+	5.13552i	0.316244	+	0.364965i
$199$	−1.22795	+	8.54058i	−0.0870471	+	0.605426i	0.898873	+	0.438209i	$0.144387\pi$
$199$	−1.22795	+	8.54058i	−0.0870471	+	0.605426i	−0.985920	+	0.167217i	$0.946522\pi$
$200$	−1.00000			−0.0707107
$201$	−1.73126	+	3.79334i	−0.122114	+	0.267562i
$202$	7.12376			0.501226
$203$	−5.19844	+	36.1559i	−0.364859	+	2.53765i
$204$	2.26303	+	2.61168i	0.158444	+	0.182854i
$205$	−1.51640	−	0.445257i	−0.105910	−	0.0310981i
$206$	4.79707	+	3.08289i	0.334227	+	0.214795i
$207$	14.6813	−	9.43512i	1.02042	−	0.655786i
$208$	−0.405117	+	2.81765i	−0.0280898	+	0.195369i
$209$	4.55853	−	9.98179i	0.315320	−	0.690455i
$210$	0.314493	−	2.18735i	0.0217021	−	0.150941i
$211$	−1.63146	+	1.88281i	−0.112315	+	0.129618i	−0.809123	−	0.587639i	$-0.800057\pi$
$211$	−1.63146	+	1.88281i	−0.112315	+	0.129618i	0.696808	+	0.717257i	$0.254603\pi$
$212$	−1.08925	−	0.700018i	−0.0748099	−	0.0480774i
$213$	1.87650	+	4.10895i	0.128575	+	0.281541i
$214$	−0.926966	−	2.02977i	−0.0633661	−	0.138752i
$215$	10.7484	+	3.15600i	0.733032	+	0.215238i
$216$	−0.416170	−	2.89453i	−0.0283168	−	0.196948i
$217$	−14.1053	−	9.06494i	−0.957532	−	0.615368i
$218$	6.66351	−	1.95658i	0.451310	−	0.132517i
$219$	−2.77114	−	0.813680i	−0.187256	−	0.0549834i
$220$	0.352880	+	2.45433i	0.0237912	+	0.165471i
$221$	12.6459	+	14.5942i	0.850656	+	0.981710i
$222$	1.86648	−	1.19951i	0.125270	−	0.0805061i
$223$	2.90914	−	3.35732i	0.194810	−	0.224823i	−0.649938	−	0.759988i	$-0.725205\pi$
$223$	2.90914	−	3.35732i	0.194810	−	0.224823i	0.844748	+	0.535165i	$0.179750\pi$
$224$	2.84079	+	3.27844i	0.189808	+	0.219050i
$225$	2.62949	−	0.772087i	0.175299	−	0.0514725i
$226$	−7.46081	−	16.3369i	−0.496286	−	1.08671i
$227$	−14.4152	+	4.23268i	−0.956769	+	0.280933i	−0.722603	−	0.691264i	$-0.757054\pi$
$227$	−14.4152	+	4.23268i	−0.956769	+	0.280933i	−0.234167	+	0.972196i	$0.575236\pi$
$228$	−1.89655	+	1.21884i	−0.125602	+	0.0807195i
$229$	8.40315	−	18.4003i	0.555296	−	1.21593i	−0.398969	−	0.916964i	$-0.630632\pi$
$229$	8.40315	−	18.4003i	0.555296	−	1.21593i	0.954265	−	0.298963i	$-0.0966409\pi$
$230$	6.36809			0.419899
$231$	−5.47946			−0.360522
$232$	−3.49796	+	7.65947i	−0.229653	+	0.502869i
$233$	−4.90135	+	5.65646i	−0.321098	+	0.370567i	−0.893234	−	0.449592i	$-0.851570\pi$
$233$	−4.90135	+	5.65646i	−0.321098	+	0.370567i	0.572136	+	0.820159i	$0.306115\pi$
$234$	−1.11022	−	7.72176i	−0.0725775	−	0.504787i
$235$	−0.635335	−	4.41885i	−0.0414447	−	0.288254i
$236$	−1.70945	+	1.97281i	−0.111276	+	0.128419i
$237$	3.48796	−	7.63756i	0.226567	−	0.496113i
$238$	29.4280			1.90753
$239$	14.0875			0.911245			0.455622	−	0.890173i	$-0.349417\pi$
$239$	14.0875			0.911245			0.455622	+	0.890173i	$0.349417\pi$
$240$	0.211618	−	0.463380i	0.0136599	−	0.0299110i
$241$	−0.192733	+	0.123862i	−0.0124150	+	0.00797866i	−0.546834	−	0.837241i	$-0.684167\pi$
$241$	−0.192733	+	0.123862i	−0.0124150	+	0.00797866i	0.534419	+	0.845220i	$0.320531\pi$
$242$	−4.65519	+	1.36689i	−0.299247	+	0.0878669i
$243$	5.06896	+	11.0995i	0.325174	+	0.712031i
$244$	1.46191	−	0.429254i	0.0935889	−	0.0274802i
$245$	−7.73931	−	8.93164i	−0.494446	−	0.570621i
$246$	0.527222	−	0.608446i	0.0336144	−	0.0387931i
$247$	−10.5980	+	6.81091i	−0.674333	+	0.433368i
$248$	−2.53114	−	2.92109i	−0.160727	−	0.185489i
$249$	−0.143106	−	0.995323i	−0.00906897	−	0.0630761i
$250$	0.959493	+	0.281733i	0.0606837	+	0.0178183i
$251$	−10.9174	+	3.20563i	−0.689098	+	0.202337i	−0.607490	−	0.794327i	$-0.707824\pi$
$251$	−10.9174	+	3.20563i	−0.689098	+	0.202337i	−0.0816078	+	0.996665i	$0.526005\pi$
$252$	−10.0011	−	6.42729i	−0.630007	−	0.404881i
$253$	−2.24717	−	15.6294i	−0.141278	−	0.982613i
$254$	−7.31625	−	2.14824i	−0.459062	−	0.134793i
$255$	−1.43557	−	3.14346i	−0.0898989	−	0.196851i
$256$	0.415415	+	0.909632i	0.0259634	+	0.0568520i
$257$	6.62962	+	4.26060i	0.413544	+	0.265769i	0.730828	−	0.682562i	$-0.239134\pi$
$257$	6.62962	+	4.26060i	0.413544	+	0.265769i	−0.317283	+	0.948331i	$0.602771\pi$
$258$	−3.73698	+	4.31270i	−0.232654	+	0.268497i
$259$	2.68884	−	18.7013i	0.167077	−	1.16204i
$260$	1.18253	−	2.58938i	0.0733374	−	0.160587i
$261$	3.28407	−	22.8412i	0.203279	−	1.41384i
$262$	−9.53948	+	6.13065i	−0.589351	+	0.378753i
$263$	−1.63377	−	1.04996i	−0.100742	−	0.0647431i	0.489300	−	0.872116i	$-0.337252\pi$
$263$	−1.63377	−	1.04996i	−0.100742	−	0.0647431i	−0.590042	+	0.807373i	$0.700889\pi$
$264$	−1.21196	−	0.355865i	−0.0745912	−	0.0219020i
$265$	0.847909	+	0.978539i	0.0520866	+	0.0601112i
$266$	−2.73216	+	19.0026i	−0.167519	+	1.16512i
$267$	8.56841			0.524378
$268$	1.16684	+	8.10176i	0.0712761	+	0.494894i
$269$	−12.5175			−0.763208			−0.381604	−	0.924326i	$-0.624628\pi$
$269$	−12.5175			−0.763208			−0.381604	+	0.924326i	$0.624628\pi$
$270$	−0.416170	+	2.89453i	−0.0253273	+	0.176155i
$271$	−2.52357	−	2.91235i	−0.153296	−	0.176913i	0.673907	−	0.738816i	$-0.264615\pi$
$271$	−2.52357	−	2.91235i	−0.153296	−	0.176913i	−0.827203	+	0.561903i	$0.810069\pi$
$272$	6.50898	+	1.91121i	0.394665	+	0.115884i
$273$	5.29198	+	3.40095i	0.320285	+	0.205835i
$274$	0.741879	−	0.476776i	0.0448185	−	0.0288031i
$275$	0.352880	−	2.45433i	0.0212795	−	0.148002i
$276$	−1.34760	+	2.95084i	−0.0811163	+	0.177620i
$277$	2.51646	−	17.5024i	0.151199	−	1.05162i	−0.763014	−	0.646382i	$-0.776281\pi$
$277$	2.51646	−	17.5024i	0.151199	−	1.05162i	0.914213	−	0.405233i	$-0.132810\pi$
$278$	−8.90624	+	10.2783i	−0.534161	+	0.616454i
$279$	8.91093	+	5.72670i	0.533483	+	0.342849i
$280$	−1.80207	−	3.94598i	−0.107694	−	0.235818i
$281$	−12.4774	−	27.3218i	−0.744342	−	1.62988i	−0.776277	−	0.630392i	$-0.782894\pi$
$281$	−12.4774	−	27.3218i	−0.744342	−	1.62988i	0.0319346	−	0.999490i	$-0.489833\pi$
$282$	2.18205	+	0.640708i	0.129939	+	0.0381536i
$283$	−4.02843	−	28.0183i	−0.239465	−	1.66552i	−0.654765	−	0.755832i	$-0.727233\pi$
$283$	−4.02843	−	28.0183i	−0.239465	−	1.66552i	0.415300	−	0.909684i	$-0.363677\pi$
$284$	7.45970	+	4.79406i	0.442652	+	0.284475i
$285$	2.16311	−	0.635147i	0.128132	−	0.0376228i
$286$	−6.77250	−	1.98858i	−0.400466	−	0.117587i
$287$	−0.975693	−	6.78609i	−0.0575933	−	0.400570i
$288$	−1.79464	−	2.07113i	−0.105750	−	0.122042i
$289$	24.4128	−	15.6891i	1.43605	−	0.922890i
$290$	5.51420	−	6.36372i	0.323805	−	0.373691i
$291$	5.01755	+	5.79056i	0.294134	+	0.339449i
$292$	−5.43986	+	1.59729i	−0.318343	+	0.0934741i
$293$	−5.14531	−	11.2667i	−0.300592	−	0.658205i	0.697715	−	0.716376i	$-0.254200\pi$
$293$	−5.14531	−	11.2667i	−0.300592	−	0.658205i	−0.998307	+	0.0581711i	$0.981473\pi$
$294$	5.77652	−	1.69614i	0.336893	−	0.0989208i
$295$	2.19601	−	1.41129i	0.127857	−	0.0821685i
$296$	1.80929	−	3.96179i	0.105163	−	0.230274i
$297$	7.25099			0.420745
$298$	−24.1600			−1.39955
$299$	−7.53046	+	16.4894i	−0.435498	+	0.953607i
$300$	−0.333595	+	0.384990i	−0.0192601	+	0.0222274i
$301$	6.91576	+	48.1002i	0.398618	+	2.77245i
$302$	−1.72947	−	12.0287i	−0.0995199	−	0.692176i
$303$	2.37645	−	2.74257i	0.136524	−	0.157557i
$304$	−1.83843	+	4.02561i	−0.105441	+	0.230885i
$305$	−1.52362			−0.0872424
$306$	−18.5909			−1.06277
$307$	11.6535	−	25.5176i	0.665101	−	1.45637i	−0.212591	−	0.977141i	$-0.568190\pi$
$307$	11.6535	−	25.5176i	0.665101	−	1.45637i	0.877692	−	0.479226i	$-0.159082\pi$
$308$	−9.04885	+	5.81534i	−0.515606	+	0.331360i
$309$	2.78716	−	0.818384i	0.158556	−	0.0465562i
$310$	1.60564	+	3.51587i	0.0911944	+	0.199688i
$311$	−4.05954	+	1.19199i	−0.230195	+	0.0675914i	−0.394796	−	0.918769i	$-0.629185\pi$
$311$	−4.05954	+	1.19199i	−0.230195	+	0.0675914i	0.164601	+	0.986360i	$0.447366\pi$
$312$	0.949621	+	1.09592i	0.0537617	+	0.0620443i
$313$	12.8796	−	14.8638i	0.727998	−	0.840154i	−0.264247	−	0.964455i	$-0.585123\pi$
$313$	12.8796	−	14.8638i	0.727998	−	0.840154i	0.992245	+	0.124301i	$0.0396688\pi$
$314$	3.92078	−	2.51973i	0.221262	−	0.142197i
$315$	7.78517	+	8.98456i	0.438644	+	0.506223i
$316$	−2.34568	−	16.3145i	−0.131955	−	0.917765i
$317$	15.7563	+	4.62647i	0.884962	+	0.259848i	0.692467	−	0.721450i	$-0.256524\pi$
$317$	15.7563	+	4.62647i	0.884962	+	0.259848i	0.192495	+	0.981298i	$0.438342\pi$
$318$	−0.632868	+	0.185827i	−0.0354895	+	0.0104206i
$319$	−17.5645	−	11.2880i	−0.983426	−	0.632009i
$320$	−0.142315	−	0.989821i	−0.00795564	−	0.0553327i
$321$	−1.09067	−	0.320251i	−0.0608755	−	0.0178746i
$322$	11.4757	+	25.1284i	0.639518	+	1.40035i
$323$	12.4715	+	27.3088i	0.693933	+	1.51950i
$324$	5.66316	+	3.63949i	0.314620	+	0.202194i
$325$	−1.86414	+	2.15134i	−0.103404	+	0.119335i
$326$	−0.188213	+	1.30905i	−0.0104241	+	0.0725015i
$327$	1.46965	−	3.21809i	0.0812720	−	0.177961i
$328$	0.224918	−	1.56434i	0.0124190	−	0.0863760i
$329$	16.2918	−	10.4701i	0.898195	−	0.577235i
$330$	1.06261	+	0.682899i	0.0584949	+	0.0375924i
$331$	−10.1029	−	2.96649i	−0.555307	−	0.163053i	−0.00797478	−	0.999968i	$-0.502538\pi$
$331$	−10.1029	−	2.96649i	−0.555307	−	0.163053i	−0.547332	+	0.836915i	$0.684357\pi$
$332$	−1.29266	−	1.49181i	−0.0709441	−	0.0818738i
$333$	−1.69865	+	11.8144i	−0.0930857	+	0.647425i
$334$	13.4920			0.738251
$335$	1.16295	−	8.10232i	0.0635390	−	0.442677i
$336$	2.20984			0.120557
$337$	−3.37872	+	23.4995i	−0.184051	+	1.28010i	0.663012	+	0.748609i	$0.269278\pi$
$337$	−3.37872	+	23.4995i	−0.184051	+	1.28010i	−0.847063	+	0.531493i	$0.821631\pi$
$338$	−3.20667	−	3.70070i	−0.174420	−	0.201291i
$339$	−8.77842	−	2.57758i	−0.476779	−	0.139995i
$340$	−5.70687	−	3.66758i	−0.309498	−	0.198903i
$341$	8.06251	−	5.18146i	0.436609	−	0.280592i
$342$	1.72602	−	12.0047i	0.0933324	−	0.649141i
$343$	8.68283	−	19.0127i	0.468829	−	1.02659i
$344$	−1.59423	+	11.0881i	−0.0859550	+	0.597830i
$345$	2.12437	−	2.45165i	0.114372	−	0.131992i
$346$	14.7494	+	9.47886i	0.792932	+	0.509587i
$347$	4.28992	+	9.39362i	0.230295	+	0.504276i	0.989137	−	0.146999i	$-0.0469615\pi$
$347$	4.28992	+	9.39362i	0.230295	+	0.504276i	−0.758841	+	0.651275i	$0.774234\pi$
$348$	1.78191	+	3.90185i	0.0955206	+	0.209161i
$349$	23.3456	+	6.85490i	1.24966	+	0.366934i	0.838638	−	0.544689i	$-0.183352\pi$
$349$	23.3456	+	6.85490i	1.24966	+	0.366934i	0.411026	+	0.911624i	$0.365171\pi$
$350$	0.617362	+	4.29385i	0.0329994	+	0.229516i
$351$	−7.00290	−	4.50049i	−0.373787	−	0.240218i
$352$	−2.37913	+	0.698576i	−0.126808	+	0.0372342i
$353$	33.1868	+	9.74452i	1.76635	+	0.518648i	0.993287	−	0.115676i	$-0.0369033\pi$
$353$	33.1868	+	9.74452i	1.76635	+	0.518648i	0.773067	+	0.634324i	$0.218721\pi$
$354$	0.189247	+	1.31624i	0.0100584	+	0.0699575i
$355$	−5.80688	−	6.70150i	−0.308197	−	0.355679i
$356$	14.1500	−	9.09365i	0.749948	−	0.481962i
$357$	9.81704	−	11.3295i	0.519573	−	0.599619i
$358$	−9.07152	−	10.4691i	−0.479445	−	0.553309i
$359$	−31.3117	+	9.19393i	−1.65257	+	0.485237i	−0.969494	−	0.245114i	$-0.921175\pi$
$359$	−31.3117	+	9.19393i	−1.65257	+	0.485237i	−0.683072	+	0.730351i	$0.739356\pi$
$360$	1.13844	+	2.49284i	0.0600012	+	0.131384i
$361$	−0.561655	+	0.164917i	−0.0295608	+	0.00867983i
$362$	−10.0758	+	6.47534i	−0.529574	+	0.340336i
$363$	−1.02671	+	2.24819i	−0.0538885	+	0.117999i
$364$	12.3487			0.647246
$365$	5.66951			0.296756
$366$	0.322427	−	0.706016i	0.0168535	−	0.0369040i
$367$	9.79584	−	11.3050i	0.511339	−	0.590116i	−0.440102	−	0.897948i	$-0.645058\pi$
$367$	9.79584	−	11.3050i	0.511339	−	0.590116i	0.951441	+	0.307831i	$0.0996033\pi$
$368$	0.906274	+	6.30327i	0.0472428	+	0.328581i
$369$	0.616386	+	4.28706i	0.0320878	+	0.223175i
$370$	−2.85216	+	3.29157i	−0.148277	+	0.171121i
$371$	−2.33331	+	5.10923i	−0.121139	+	0.265258i
$372$	−1.96896			−0.102086
$373$	0.102015			0.00528213			0.00264106	−	0.999997i	$-0.499159\pi$
$373$	0.102015			0.00528213			0.00264106	+	0.999997i	$0.499159\pi$
$374$	−6.98763	+	15.3008i	−0.361322	+	0.791184i
$375$	0.428547	−	0.275410i	0.0221301	−	0.0142221i
$376$	4.28345	−	1.25774i	0.220902	−	0.0648628i
$377$	9.95739	+	21.8037i	0.512832	+	1.12295i
$378$	−12.1717	+	3.57394i	−0.626046	+	0.183824i
$379$	−22.4329	−	25.8890i	−1.15230	−	1.32983i	−0.935382	−	0.353639i	$-0.884944\pi$
$379$	−22.4329	−	25.8890i	−1.15230	−	1.32983i	−0.216921	−	0.976189i	$-0.569601\pi$
$380$	2.89811	−	3.34460i	0.148670	−	0.171574i
$381$	−3.26772	+	2.10004i	−0.167410	+	0.107588i
$382$	0.889977	+	1.02709i	0.0455352	+	0.0525504i
$383$	−1.06117	−	7.38060i	−0.0542232	−	0.377131i	−0.998806	−	0.0488569i	$-0.984442\pi$
$383$	−1.06117	−	7.38060i	−0.0542232	−	0.377131i	0.944583	−	0.328274i	$-0.106467\pi$
$384$	0.488779	+	0.143519i	0.0249429	+	0.00732390i
$385$	10.3207	−	3.03042i	0.525990	−	0.154445i
$386$	4.47175	+	2.87382i	0.227606	+	0.146273i
$387$	−4.36898	−	30.3869i	−0.222088	−	1.54465i
$388$	14.4316	+	4.23749i	0.732652	+	0.215126i
$389$	−5.79751	−	12.6948i	−0.293946	−	0.643651i	0.703826	−	0.710372i	$-0.251473\pi$
$389$	−5.79751	−	12.6948i	−0.293946	−	0.643651i	−0.997772	+	0.0667214i	$0.978746\pi$
$390$	−0.602398	−	1.31907i	−0.0305036	−	0.0667936i
$391$	36.3419	+	23.3555i	1.83789	+	1.18114i
$392$	7.73931	−	8.93164i	0.390894	−	0.451116i
$393$	−0.822089	+	5.71776i	−0.0414689	+	0.288423i
$394$	4.47980	−	9.80938i	0.225689	−	0.494190i
$395$	−2.34568	+	16.3145i	−0.118024	+	0.820874i
$396$	5.71654	−	3.67380i	0.287267	−	0.184615i
$397$	−32.8843	−	21.1334i	−1.65042	−	1.06066i	−0.930298	−	0.366805i	$-0.880452\pi$
$397$	−32.8843	−	21.1334i	−1.65042	−	1.06066i	−0.720117	−	0.693852i	$-0.755912\pi$
$398$	8.27890	+	2.43090i	0.414984	+	0.121850i
$399$	6.40436	+	7.39102i	0.320619	+	0.370014i
$400$	−0.142315	+	0.989821i	−0.00711574	+	0.0494911i
$401$	27.6756			1.38205			0.691026	−	0.722830i	$-0.257159\pi$
$401$	27.6756			1.38205			0.691026	+	0.722830i	$0.257159\pi$
$402$	3.50835	+	2.25349i	0.174980	+	0.112394i
$403$	−11.0026			−0.548080
$404$	1.01382	−	7.05125i	0.0504393	−	0.350813i
$405$	−4.40840	−	5.08757i	−0.219055	−	0.252803i
$406$	35.0481	+	10.2911i	1.73941	+	0.510737i
$407$	9.08509	+	5.83863i	0.450331	+	0.289410i
$408$	2.90716	−	1.86832i	0.143926	−	0.0924956i
$409$	−0.614218	+	4.27198i	−0.0303711	+	0.211236i	−0.999356	−	0.0358844i	$-0.988575\pi$
$409$	−0.614218	+	4.27198i	−0.0303711	+	0.211236i	0.968985	+	0.247120i	$0.0794843\pi$
$410$	−0.656531	+	1.43760i	−0.0324238	+	0.0709982i
$411$	0.0639333	−	0.444666i	0.00315360	−	0.0219338i
$412$	3.73420	−	4.30950i	0.183971	−	0.212314i
$413$	9.52630	+	6.12218i	0.468759	+	0.301253i
$414$	−7.24971	−	15.8747i	−0.356304	−	0.780197i
$415$	0.820009	+	1.79557i	0.0402526	+	0.0881410i
$416$	2.73132	+	0.801987i	0.133914	+	0.0393206i
$417$	0.985977	+	6.85762i	0.0482835	+	0.335819i
$418$	−9.23144	−	5.93269i	−0.451525	−	0.290177i
$419$	38.5846	−	11.3294i	1.88498	−	0.553480i	0.889685	−	0.456575i	$-0.150924\pi$
$419$	38.5846	−	11.3294i	1.88498	−	0.553480i	0.995294	−	0.0969048i	$-0.0308942\pi$
$420$	−2.12033	−	0.622584i	−0.103461	−	0.0303790i
$421$	−3.16716	−	22.0281i	−0.154358	−	1.07358i	−0.908805	−	0.417222i	$-0.863004\pi$
$421$	−3.16716	−	22.0281i	−0.154358	−	1.07358i	0.754447	−	0.656361i	$-0.227905\pi$
$422$	1.63146	+	1.88281i	0.0794184	+	0.0916537i
$423$	−10.2922	+	6.61440i	−0.500424	+	0.321603i
$424$	−0.847909	+	0.978539i	−0.0411781	+	0.0475221i
$425$	4.44242	+	5.12683i	0.215489	+	0.248688i
$426$	4.33418	−	1.27263i	0.209992	−	0.0616592i
$427$	−2.74568	−	6.01219i	−0.132873	−	0.290950i
$428$	−2.14103	+	0.628664i	−0.103491	+	0.0303876i
$429$	−3.02486	+	1.94396i	−0.146042	+	0.0938552i
$430$	4.65353	−	10.1898i	0.224413	−	0.491396i
$431$	−14.6503			−0.705680			−0.352840	−	0.935684i	$-0.614784\pi$
$431$	−14.6503			−0.705680			−0.352840	+	0.935684i	$0.614784\pi$
$432$	−2.92429			−0.140695
$433$	−1.57833	+	3.45607i	−0.0758498	+	0.166088i	−0.943758	−	0.330636i	$-0.892737\pi$
$433$	−1.57833	+	3.45607i	−0.0758498	+	0.166088i	0.867908	+	0.496724i	$0.165464\pi$
$434$	−10.9801	+	12.6717i	−0.527060	+	0.608260i
$435$	−0.610456	−	4.24582i	−0.0292691	−	0.203571i
$436$	−0.988352	−	6.87414i	−0.0473335	−	0.329212i
$437$	−18.4554	+	21.2987i	−0.882843	+	1.01885i
$438$	−1.19977	+	2.62714i	−0.0573273	+	0.125529i
$439$	−36.9728			−1.76462			−0.882308	−	0.470672i	$-0.844012\pi$
$439$	−36.9728			−1.76462			−0.882308	+	0.470672i	$0.844012\pi$
$440$	2.47957			0.118209
$441$	−13.4544	+	29.4611i	−0.640686	+	1.40291i
$442$	16.2453	−	10.4402i	0.772711	−	0.496591i
$443$	20.6857	−	6.07387i	0.982808	−	0.288578i	0.249425	−	0.968394i	$-0.419758\pi$
$443$	20.6857	−	6.07387i	0.982808	−	0.288578i	0.733383	+	0.679816i	$0.237940\pi$
$444$	−0.921677	−	2.01819i	−0.0437409	−	0.0957791i
$445$	−16.1388	+	4.73878i	−0.765052	+	0.224640i
$446$	−2.90914	−	3.35732i	−0.137752	−	0.158974i
$447$	−8.05966	+	9.30134i	−0.381209	+	0.439938i
$448$	3.64936	−	2.34530i	0.172416	−	0.110805i
$449$	10.6741	+	12.3186i	0.503742	+	0.581350i	0.949485	−	0.313811i	$-0.101606\pi$
$449$	10.6741	+	12.3186i	0.503742	+	0.581350i	−0.445743	+	0.895161i	$0.647060\pi$
$450$	−0.390013	−	2.71260i	−0.0183854	−	0.127873i
$451$	3.76003	+	1.10405i	0.177053	+	0.0519875i
$452$	−17.2324	+	5.05989i	−0.810543	+	0.237997i
$453$	−5.20788	−	3.34690i	−0.244688	−	0.157251i
$454$	2.13810	+	14.8708i	0.100346	+	0.697922i
$455$	−11.8485	−	3.47902i	−0.555464	−	0.163099i
$456$	0.936525	+	2.05070i	0.0438568	+	0.0960330i
$457$	6.87246	+	15.0486i	0.321480	+	0.703943i	0.999517	−	0.0310849i	$-0.00989623\pi$
$457$	6.87246	+	15.0486i	0.321480	+	0.703943i	−0.678037	+	0.735028i	$0.737169\pi$
$458$	−17.0171	−	10.9363i	−0.795159	−	0.511018i
$459$	−12.9909	+	14.9923i	−0.606365	+	0.699783i
$460$	0.906274	−	6.30327i	0.0422552	−	0.293892i
$461$	8.19247	−	17.9390i	0.381562	−	0.835503i	−0.617250	−	0.786767i	$-0.711753\pi$
$461$	8.19247	−	17.9390i	0.381562	−	0.835503i	0.998812	−	0.0487362i	$-0.0155194\pi$
$462$	−0.779808	+	5.42368i	−0.0362800	+	0.252333i
$463$	−28.8464	+	18.5385i	−1.34061	+	0.861556i	−0.996988	−	0.0775532i	$-0.975289\pi$
$463$	−28.8464	+	18.5385i	−1.34061	+	0.861556i	−0.343619	+	0.939109i	$0.611653\pi$
$464$	7.08370	+	4.55242i	0.328853	+	0.211341i
$465$	1.88921	+	0.554721i	0.0876099	+	0.0257246i
$466$	4.90135	+	5.65646i	0.227051	+	0.262031i
$467$	−0.388004	+	2.69863i	−0.0179547	+	0.124878i	−0.996827	−	0.0795926i	$-0.974638\pi$
$467$	−0.388004	+	2.69863i	−0.0179547	+	0.124878i	0.978873	+	0.204470i	$0.0655472\pi$
$468$	−7.80117			−0.360609
$469$	34.0673	−	10.0119i	1.57308	−	0.462309i
$470$	−4.46429			−0.205922
$471$	0.337883	−	2.35003i	0.0155688	−	0.108284i
$472$	1.70945	+	1.97281i	0.0786839	+	0.0908060i
$473$	−26.6513	−	7.82554i	−1.22543	−	0.359819i
$474$	−7.06344	−	4.53939i	−0.324434	−	0.208501i
$475$	−3.72300	+	2.39263i	−0.170823	+	0.109781i
$476$	4.18804	−	29.1285i	0.191958	−	1.33510i
$477$	1.47405	−	3.22772i	0.0674920	−	0.147787i
$478$	2.00486	−	13.9441i	0.0917002	−	0.637789i
$479$	13.1941	−	15.2268i	0.602852	−	0.695728i	−0.369505	−	0.929229i	$-0.620473\pi$
$479$	13.1941	−	15.2268i	0.602852	−	0.695728i	0.972357	+	0.233501i	$0.0750181\pi$
$480$	−0.428547	−	0.275410i	−0.0195604	−	0.0125707i
$481$	−5.15036	−	11.2777i	−0.234836	−	0.514220i
$482$	0.0951725	+	0.208399i	0.00433499	+	0.00949231i
$483$	13.5024	+	3.96467i	0.614382	+	0.180399i
$484$	0.690472	+	4.80234i	0.0313851	+	0.218288i
$485$	−12.6532	−	8.13169i	−0.574550	−	0.369241i
$486$	11.7079	−	3.43774i	0.531080	−	0.155939i
$487$	−24.4523	−	7.17983i	−1.10804	−	0.325349i	−0.323997	−	0.946058i	$-0.605027\pi$
$487$	−24.4523	−	7.17983i	−1.10804	−	0.325349i	−0.784041	+	0.620709i	$0.786845\pi$
$488$	−0.216834	−	1.50811i	−0.00981562	−	0.0682691i
$489$	0.441183	+	0.509152i	0.0199510	+	0.0230247i
$490$	−9.94215	+	6.38943i	−0.449140	+	0.288645i
$491$	−12.8161	+	14.7905i	−0.578380	+	0.667487i	−0.967256	−	0.253804i	$-0.918318\pi$
$491$	−12.8161	+	14.7905i	−0.578380	+	0.667487i	0.388875	+	0.921290i	$0.372864\pi$
$492$	−0.527222	−	0.608446i	−0.0237690	−	0.0274309i
$493$	54.8083	−	16.0932i	2.46844	−	0.724799i
$494$	5.23333	+	11.4594i	0.235459	+	0.515583i
$495$	−6.52000	+	1.91445i	−0.293052	+	0.0860480i
$496$	−3.25157	+	2.08966i	−0.146000	+	0.0938285i
$497$	15.9796	−	34.9905i	0.716783	−	1.56954i
$498$	−1.00556			−0.0450602
$499$	−8.18388			−0.366361			−0.183180	−	0.983079i	$-0.558639\pi$
$499$	−8.18388			−0.366361			−0.183180	+	0.983079i	$0.558639\pi$
$500$	0.415415	−	0.909632i	0.0185779	−	0.0406800i
$501$	4.50088	−	5.19429i	0.201084	−	0.232064i
$502$	1.61930	+	11.2625i	0.0722727	+	0.502668i
$503$	−1.10879	−	7.71183i	−0.0494387	−	0.343853i	−0.999495	−	0.0317751i	$-0.989884\pi$
$503$	−1.10879	−	7.71183i	−0.0494387	−	0.343853i	0.950056	−	0.312078i	$-0.101025\pi$
$504$	−7.78517	+	8.98456i	−0.346779	+	0.400204i
$505$	−2.95932	+	6.48000i	−0.131688	+	0.288356i
$506$	−15.7901			−0.701957
$507$	−2.49446			−0.110783
$508$	−3.16759	+	6.93605i	−0.140539	+	0.307738i
$509$	10.4897	−	6.74133i	0.464949	−	0.298804i	−0.287113	−	0.957897i	$-0.592696\pi$
$509$	10.4897	−	6.74133i	0.464949	−	0.298804i	0.752062	+	0.659092i	$0.229059\pi$
$510$	−3.31577	+	0.973597i	−0.146825	+	0.0431116i
$511$	10.2169	+	22.3718i	0.451967	+	0.989670i
$512$	0.959493	−	0.281733i	0.0424040	−	0.0124509i
$513$	−8.47492	−	9.78058i	−0.374177	−	0.431823i
$514$	5.16073	−	5.95580i	0.227630	−	0.262699i
$515$	−4.79707	+	3.08289i	−0.211384	+	0.135848i
$516$	3.73698	+	4.31270i	0.164511	+	0.189856i
$517$	1.57536	+	10.9569i	0.0692842	+	0.481882i
$518$	−18.1283	−	5.32295i	−0.796511	−	0.233877i
$519$	8.56959	−	2.51626i	0.376163	−	0.110452i
$520$	−2.39473	−	1.53900i	−0.105016	−	0.0674897i
$521$	0.907461	+	6.31153i	0.0397566	+	0.276513i	0.999996	−	0.00266318i	$-0.000847719\pi$
$521$	0.907461	+	6.31153i	0.0397566	+	0.276513i	−0.960240	+	0.279176i	$0.909939\pi$
$522$	−22.1414	−	6.50129i	−0.969101	−	0.284554i
$523$	0.869622	+	1.90421i	0.0380259	+	0.0832652i	0.927692	−	0.373347i	$-0.121790\pi$
$523$	0.869622	+	1.90421i	0.0380259	+	0.0832652i	−0.889666	+	0.456612i	$0.849063\pi$
$524$	4.71064	+	10.3149i	0.205785	+	0.450607i
$525$	1.85904	+	1.19473i	0.0811350	+	0.0521423i
$526$	−1.27178	+	1.46771i	−0.0554522	+	0.0639953i
$527$	−3.73154	+	25.9534i	−0.162548	+	1.13055i
$528$	−0.524723	+	1.14898i	−0.0228356	+	0.0500031i
$529$	−2.49799	+	17.3739i	−0.108608	+	0.755388i
$530$	1.08925	−	0.700018i	0.0473139	−	0.0304068i
$531$	−6.01816	−	3.86764i	−0.261166	−	0.167841i
$532$	18.4203	+	5.40870i	0.798622	+	0.234497i
$533$	−2.94613	−	3.40002i	−0.127611	−	0.147271i
$534$	1.21941	−	8.48120i	0.0527691	−	0.367017i
$535$	2.23142			0.0964728
$536$	8.18535	−	0.00196287i	0.353553	−	8.47830e-5i
$537$	−7.05671			−0.304520
$538$	−1.78143	+	12.3901i	−0.0768030	+	0.534177i
$539$	19.1902	+	22.1466i	0.826579	+	0.953923i
$540$	2.80584	+	0.823868i	0.120744	+	0.0354536i
$541$	−34.1277	−	21.9326i	−1.46727	−	0.942954i	−0.998211	−	0.0597845i	$-0.980959\pi$
$541$	−34.1277	−	21.9326i	−1.46727	−	0.942954i	−0.469054	−	0.883170i	$-0.655405\pi$
$542$	−3.24185	+	2.08341i	−0.139249	+	0.0894900i
$543$	−0.868311	+	6.03923i	−0.0372628	+	0.259168i
$544$	2.81808	−	6.17073i	0.120824	−	0.264568i
$545$	−0.988352	+	6.87414i	−0.0423364	+	0.294456i
$546$	4.11946	−	4.75411i	0.176296	−	0.203457i
$547$	26.9369	+	17.3113i	1.15174	+	0.740178i	0.969985	−	0.243166i	$-0.0781859\pi$
$547$	26.9369	+	17.3113i	1.15174	+	0.740178i	0.181755	+	0.983344i	$0.441822\pi$
$548$	−0.366343	−	0.802180i	−0.0156494	−	0.0342674i
$549$	1.73456	+	3.79815i	0.0740292	+	0.162101i
$550$	−2.37913	−	0.698576i	−0.101447	−	0.0297874i
$551$	5.30334	+	36.8855i	0.225930	+	1.57138i
$552$	2.72902	+	1.75384i	0.116155	+	0.0746483i
$553$	−68.6040	+	20.1440i	−2.91734	+	0.856608i
$554$	−16.9661	−	4.98169i	−0.720820	−	0.211652i
$555$	0.315752	+	2.19611i	0.0134029	+	0.0932195i
$556$	8.90624	+	10.2783i	0.377709	+	0.435899i
$557$	31.9079	−	20.5060i	1.35198	−	0.868866i	0.354183	−	0.935176i	$-0.384759\pi$
$557$	31.9079	−	20.5060i	1.35198	−	0.868866i	0.997799	+	0.0663096i	$0.0211225\pi$
$558$	6.93657	−	8.00523i	0.293649	−	0.338888i
$559$	20.8824	+	24.0995i	0.883230	+	1.01930i
$560$	−4.16228	+	1.22216i	−0.175888	+	0.0516455i
$561$	3.55960	+	7.79443i	0.150286	+	0.329081i
$562$	−28.8194	+	8.46215i	−1.21567	+	0.356954i
$563$	33.4619	−	21.5047i	1.41025	−	0.906314i	0.410268	−	0.911965i	$-0.365435\pi$
$563$	33.4619	−	21.5047i	1.41025	−	0.906314i	0.999984	+	0.00565138i	$0.00179890\pi$
$564$	0.944725	−	2.06866i	0.0397801	−	0.0871063i
$565$	17.9599			0.755578
$566$	−28.3064			−1.18981
$567$	12.1312	−	26.5636i	0.509463	−	1.11557i
$568$	5.80688	−	6.70150i	0.243651	−	0.281189i
$569$	0.454529	+	3.16132i	0.0190549	+	0.132529i	0.997128	−	0.0757308i	$-0.0241290\pi$
$569$	0.454529	+	3.16132i	0.0190549	+	0.132529i	−0.978073	+	0.208260i	$0.933220\pi$
$570$	−0.320839	−	2.23148i	−0.0134385	−	0.0934666i
$571$	−11.9408	+	13.7805i	−0.499708	+	0.576694i	−0.948434	−	0.316975i	$-0.897333\pi$
$571$	−11.9408	+	13.7805i	−0.499708	+	0.576694i	0.448725	+	0.893670i	$0.351878\pi$
$572$	−2.93217	+	6.42056i	−0.122600	+	0.268457i
$573$	0.692311			0.0289217
$574$	−6.85588			−0.286159
$575$	−2.64540	+	5.79262i	−0.110321	+	0.241569i
$576$	−2.30545	+	1.48162i	−0.0960605	+	0.0617344i
$577$	−32.6840	+	9.59690i	−1.36065	+	0.399524i	−0.878993	−	0.476834i	$-0.841784\pi$
$577$	−32.6840	+	9.59690i	−1.36065	+	0.399524i	−0.481661	+	0.876358i	$0.659966\pi$
$578$	−12.0551	−	26.3971i	−0.501428	−	1.09797i
$579$	2.59814	−	0.762884i	0.107975	−	0.0317044i
$580$	−5.51420	−	6.36372i	−0.228965	−	0.264239i
$581$	−5.60757	+	6.47148i	−0.232641	+	0.268482i
$582$	6.44570	−	4.14240i	0.267183	−	0.171708i
$583$	−2.10245	−	2.42636i	−0.0870746	−	0.100489i
$584$	0.806855	+	5.61180i	0.0333879	+	0.232218i
$585$	7.48517	+	2.19784i	0.309473	+	0.0908696i
$586$	−11.8842	+	3.48952i	−0.490933	+	0.144151i
$587$	10.2847	+	6.60960i	0.424497	+	0.272807i	0.735399	−	0.677634i	$-0.236995\pi$
$587$	10.2847	+	6.60960i	0.424497	+	0.272807i	−0.310902	+	0.950442i	$0.600631\pi$
$588$	−0.856790	−	5.95911i	−0.0353334	−	0.245749i
$589$	−16.4125	−	4.81914i	−0.676265	−	0.198569i
$590$	−1.08440	−	2.37451i	−0.0446441	−	0.0977569i
$591$	−2.28207	−	4.99704i	−0.0938719	−	0.205551i
$592$	−3.66397	−	2.35469i	−0.150588	−	0.0967773i
$593$	−22.7987	+	26.3111i	−0.936229	+	1.08047i	0.0603796	+	0.998175i	$0.480769\pi$
$593$	−22.7987	+	26.3111i	−0.936229	+	1.08047i	−0.996608	+	0.0822902i	$0.973777\pi$
$594$	1.03192	−	7.17719i	0.0423403	−	0.294484i
$595$	−12.2248	+	26.7686i	−0.501169	+	1.09741i
$596$	−3.43832	+	23.9141i	−0.140839	+	0.979558i
$597$	3.69767	−	2.37635i	0.151336	−	0.0972576i
$598$	15.2499	+	9.80050i	0.623614	+	0.400772i
$599$	−10.9090	−	3.20317i	−0.445730	−	0.130878i	0.0511624	−	0.998690i	$-0.483707\pi$
$599$	−10.9090	−	3.20317i	−0.445730	−	0.130878i	−0.496892	+	0.867812i	$0.665526\pi$
$600$	0.333595	+	0.384990i	0.0136190	+	0.0157171i
$601$	−2.39260	+	16.6409i	−0.0975961	+	0.678796i	0.881017	+	0.473085i	$0.156860\pi$
$601$	−2.39260	+	16.6409i	−0.0975961	+	0.678796i	−0.978613	+	0.205711i	$0.934049\pi$
$602$	48.5948			1.98058
$603$	−21.5218	+	6.32497i	−0.876434	+	0.257573i
$604$	−12.1524			−0.494475
$605$	0.690472	−	4.80234i	0.0280717	−	0.195243i
$606$	−2.37645	−	2.74257i	−0.0965368	−	0.111409i
$607$	44.5094	+	13.0692i	1.80658	+	0.530461i	0.998297	−	0.0583305i	$-0.0185777\pi$
$607$	44.5094	+	13.0692i	1.80658	+	0.530461i	0.808285	+	0.588791i	$0.200396\pi$
$608$	3.72300	+	2.39263i	0.150987	+	0.0970338i
$609$	15.6538	−	10.0601i	0.634326	−	0.407656i
$610$	−0.216834	+	1.50811i	−0.00877936	+	0.0610618i
$611$	5.27916	−	11.5597i	0.213572	−	0.467657i
$612$	−2.64576	+	18.4017i	−0.106949	+	0.743843i
$613$	−23.3484	+	26.9455i	−0.943034	+	1.08832i	0.0529334	+	0.998598i	$0.483143\pi$
$613$	−23.3484	+	26.9455i	−0.943034	+	1.08832i	−0.995967	+	0.0897207i	$0.971403\pi$
$614$	−23.5994	−	15.1664i	−0.952395	−	0.612067i
$615$	0.334446	+	0.732336i	0.0134862	+	0.0295306i
$616$	4.46836	+	9.78435i	0.180036	+	0.394223i
$617$	−32.2784	−	9.47778i	−1.29948	−	0.381561i	−0.442432	−	0.896802i	$-0.645884\pi$
$617$	−32.2784	−	9.47778i	−1.29948	−	0.381561i	−0.857046	+	0.515241i	$0.827703\pi$
$618$	−0.413400	−	2.87526i	−0.0166294	−	0.115660i
$619$	−0.216717	−	0.139275i	−0.00871058	−	0.00559795i	0.536278	−	0.844041i	$-0.319830\pi$
$619$	−0.216717	−	0.139275i	−0.00871058	−	0.00559795i	−0.544989	+	0.838443i	$0.683466\pi$
$620$	3.70859	−	1.08894i	0.148940	−	0.0437329i
$621$	−17.8678	−	5.24647i	−0.717011	−	0.210533i
$622$	0.602122	+	4.18785i	0.0241429	+	0.167918i
$623$	−47.7824	−	55.1438i	−1.91436	−	2.20929i
$624$	1.21991	−	0.783989i	0.0488355	−	0.0313847i
$625$	−0.654861	+	0.755750i	−0.0261944	+	0.0302300i
$626$	−12.8796	−	14.8638i	−0.514772	−	0.594079i
$627$	−5.36359	+	1.57489i	−0.214201	+	0.0628951i
$628$	−1.93610	−	4.23947i	−0.0772588	−	0.169173i
$629$	−28.3490	+	8.32403i	−1.13035	+	0.331901i
$630$	10.0011	−	6.42729i	0.398452	−	0.256069i
$631$	6.98355	−	15.2918i	0.278011	−	0.608758i	−0.718190	−	0.695847i	$-0.755029\pi$
$631$	6.98355	−	15.2918i	0.278011	−	0.608758i	0.996201	+	0.0870888i	$0.0277564\pi$
$632$	−16.4823			−0.655631
$633$	1.26911			0.0504426
$634$	6.82173	−	14.9375i	0.270926	−	0.593244i
$635$	4.99339	−	5.76268i	0.198157	−	0.228685i
$636$	0.0938689	+	0.652872i	0.00372214	+	0.0258881i
$637$	−4.78777	−	33.2997i	−0.189699	−	1.31938i
$638$	−13.6728	+	15.7793i	−0.541313	+	0.624709i
$639$	−10.0950	+	22.1049i	−0.399351	+	0.874458i
$640$	−1.00000			−0.0395285
$641$	3.95268			0.156121			0.0780606	−	0.996949i	$-0.475127\pi$
$641$	3.95268			0.156121			0.0780606	+	0.996949i	$0.475127\pi$
$642$	−0.472210	+	1.03400i	−0.0186366	+	0.0408086i
$643$	28.6403	−	18.4060i	1.12947	−	0.725863i	0.164017	−	0.986458i	$-0.447555\pi$
$643$	28.6403	−	18.4060i	1.12947	−	0.725863i	0.965448	+	0.260594i	$0.0839185\pi$
$644$	26.5058	−	7.78280i	1.04447	−	0.306685i
$645$	−2.37057	−	5.19083i	−0.0933413	−	0.204389i
$646$	28.8057	−	8.45812i	1.13335	−	0.332780i
$647$	−6.32220	−	7.29621i	−0.248551	−	0.286844i	0.617740	−	0.786382i	$-0.288048\pi$
$647$	−6.32220	−	7.29621i	−0.248551	−	0.286844i	−0.866292	+	0.499539i	$0.833503\pi$
$648$	4.40840	−	5.08757i	0.173178	−	0.199858i
$649$	−5.44517	+	3.49940i	−0.213742	+	0.137363i
$650$	1.86414	+	2.15134i	0.0731177	+	0.0843823i
$651$	1.21556	+	8.45443i	0.0476417	+	0.331355i
$652$	1.26894	+	0.372594i	0.0496955	+	0.0145919i
$653$	−20.0080	+	5.87489i	−0.782975	+	0.229902i	−0.648702	−	0.761042i	$-0.724688\pi$
$653$	−20.0080	+	5.87489i	−0.782975	+	0.229902i	−0.134273	+	0.990944i	$0.542870\pi$
$654$	−2.97618	−	1.91268i	−0.116378	−	0.0747916i
$655$	−1.61379	−	11.2242i	−0.0630561	−	0.438565i
$656$	−1.51640	−	0.445257i	−0.0592057	−	0.0173843i
$657$	−6.45442	−	14.1332i	−0.251811	−	0.551389i
$658$	−8.04496	−	17.6160i	−0.313625	−	0.686744i
$659$	−4.17049	−	2.68021i	−0.162459	−	0.104406i	0.456885	−	0.889526i	$-0.348965\pi$
$659$	−4.17049	−	2.68021i	−0.162459	−	0.104406i	−0.619344	+	0.785120i	$0.712601\pi$
$660$	0.827174	−	0.954610i	0.0321977	−	0.0371581i
$661$	−3.85505	+	26.8125i	−0.149944	+	1.04288i	0.766363	+	0.642408i	$0.222064\pi$
$661$	−3.85505	+	26.8125i	−0.149944	+	1.04288i	−0.916307	+	0.400477i	$0.868845\pi$
$662$	−4.37409	+	9.57792i	−0.170004	+	0.372256i
$663$	1.39998	−	9.73709i	0.0543708	−	0.378157i
$664$	−1.66059	+	1.06720i	−0.0644435	+	0.0414153i
$665$	−16.1504	−	10.3792i	−0.626284	−	0.402489i
$666$	11.4524	+	3.36273i	0.443772	+	0.130303i
$667$	35.1149	+	40.5248i	1.35965	+	1.56912i
$668$	1.92012	−	13.3547i	0.0742915	−	0.516709i
$669$	−2.26301			−0.0874930
$670$	−7.85434	−	2.30420i	−0.303440	−	0.0890189i
$671$	3.77793			0.145845
$672$	0.314493	−	2.18735i	0.0121318	−	0.0843787i
$673$	11.0101	+	12.7064i	0.424410	+	0.489795i	0.927175	−	0.374628i	$-0.122230\pi$
$673$	11.0101	+	12.7064i	0.424410	+	0.489795i	−0.502766	+	0.864423i	$0.667684\pi$
$674$	22.7795	+	6.68867i	0.877434	+	0.257638i
$675$	−2.46007	−	1.58099i	−0.0946882	−	0.0608524i
$676$	−4.11939	+	2.64737i	−0.158438	+	0.101822i
$677$	−2.48026	+	17.2506i	−0.0953240	+	0.662993i	0.884999	+	0.465593i	$0.154159\pi$
$677$	−2.48026	+	17.2506i	−0.0953240	+	0.662993i	−0.980323	+	0.197400i	$0.936750\pi$
$678$	−3.80064	+	8.32224i	−0.145963	+	0.319614i
$679$	9.28564	−	64.5830i	0.356350	−	2.47847i
$680$	−4.44242	+	5.12683i	−0.170359	+	0.196605i
$681$	6.43838	+	4.13769i	0.246719	+	0.158557i
$682$	−3.98131	−	8.71784i	−0.152452	−	0.333824i
$683$	15.7839	+	34.5620i	0.603956	+	1.32248i	0.926632	+	0.375969i	$0.122690\pi$
$683$	15.7839	+	34.5620i	0.603956	+	1.32248i	−0.322676	+	0.946509i	$0.604583\pi$
$684$	−11.6369	−	3.41690i	−0.444948	−	0.130648i
$685$	0.125504	+	0.872896i	0.00479524	+	0.0333517i
$686$	−17.5835	−	11.3002i	−0.671342	−	0.431445i
$687$	−9.88719	+	2.90314i	−0.377220	+	0.110762i
$688$	10.7484	+	3.15600i	0.409777	+	0.120321i
$689$	0.524542	+	3.64827i	0.0199835	+	0.138988i
$690$	−2.12437	−	2.45165i	−0.0808732	−	0.0933327i
$691$	7.47578	−	4.80439i	0.284392	−	0.182768i	−0.390666	−	0.920533i	$-0.627755\pi$
$691$	7.47578	−	4.80439i	0.284392	−	0.182768i	0.675058	+	0.737765i	$0.264119\pi$
$692$	11.4814	−	13.2503i	0.436459	−	0.503700i
$693$	−19.3039	−	22.2779i	−0.733294	−	0.846266i
$694$	9.90853	−	2.90941i	0.376123	−	0.110440i
$695$	−5.64973	−	12.3712i	−0.214306	−	0.469266i
$696$	4.11572	−	1.20849i	0.156006	−	0.0458075i
$697$	−9.01927	+	5.79633i	−0.341629	+	0.219552i
$698$	10.1076	−	22.1325i	0.382577	−	0.837726i
$699$	3.81275			0.144211
$700$	4.33800			0.163961
$701$	1.86157	−	4.07627i	0.0703105	−	0.153958i	−0.871214	−	0.490904i	$-0.836667\pi$
$701$	1.86157	−	4.07627i	0.0703105	−	0.153958i	0.941524	+	0.336946i	$0.109394\pi$
$702$	−5.45130	+	6.29113i	−0.205746	+	0.237443i
$703$	−2.74310	−	19.0787i	−0.103458	−	0.719566i
$704$	0.352880	+	2.45433i	0.0132997	+	0.0925012i
$705$	−1.48927	+	1.71870i	−0.0560890	+	0.0647302i
$706$	14.3683	−	31.4622i	0.540758	−	1.18410i
$707$	−30.9029			−1.16222
$708$	1.32978			0.0499761
$709$	6.88871	−	15.0842i	0.258711	−	0.566498i	−0.735052	−	0.678011i	$-0.762842\pi$
$709$	6.88871	−	15.0842i	0.258711	−	0.566498i	0.993763	+	0.111513i	$0.0355695\pi$
$710$	−7.45970	+	4.79406i	−0.279957	+	0.179918i
$711$	43.3400	−	12.7258i	1.62538	−	0.477254i
$712$	−6.98733	−	15.3001i	−0.261861	−	0.573396i
$713$	−23.6166	+	6.93446i	−0.884449	+	0.259698i
$714$	−9.81704	−	11.3295i	−0.367394	−	0.423995i
$715$	4.62228	−	5.33439i	0.172863	−	0.199495i
$716$	−11.6535	+	7.48928i	−0.435513	+	0.279887i
$717$	−4.69953	−	5.42354i	−0.175507	−	0.202546i
$718$	4.64424	+	32.3014i	0.173321	+	1.20548i
$719$	−47.6301	−	13.9855i	−1.77630	−	0.521570i	−0.781548	−	0.623845i	$-0.785569\pi$
$719$	−47.6301	−	13.9855i	−1.77630	−	0.521570i	−0.994756	+	0.102276i	$0.967388\pi$
$720$	2.62949	−	0.772087i	0.0979952	−	0.0287740i
$721$	−20.8097	−	13.3736i	−0.774993	−	0.498058i
$722$	0.0833063	+	0.579408i	0.00310034	+	0.0215633i
$723$	0.111981	+	0.0328804i	0.00416460	+	0.00122284i
$724$	4.97549	+	10.8948i	0.184913	+	0.404902i
$725$	3.49796	+	7.65947i	0.129911	+	0.284466i
$726$	2.07919	+	1.33621i	0.0771659	+	0.0495915i
$727$	−25.6246	+	29.5723i	−0.950362	+	1.09678i	0.0448457	+	0.998994i	$0.485720\pi$
$727$	−25.6246	+	29.5723i	−0.950362	+	1.09678i	−0.995208	+	0.0977825i	$0.968825\pi$
$728$	1.75740	−	12.2230i	0.0651335	−	0.453013i
$729$	−5.80729	+	12.7162i	−0.215085	+	0.470970i
$730$	0.806855	−	5.61180i	0.0298631	−	0.207702i
$731$	63.9290	−	41.0847i	2.36450	−	1.51957i
$732$	−0.652943	−	0.419621i	−0.0241335	−	0.0155096i
$733$	2.02625	+	0.594961i	0.0748413	+	0.0219754i	0.318939	−	0.947775i	$-0.396674\pi$
$733$	2.02625	+	0.594961i	0.0748413	+	0.0219754i	−0.244098	+	0.969751i	$0.578492\pi$
$734$	−9.79584	−	11.3050i	−0.361571	−	0.417275i
$735$	−0.856790	+	5.95911i	−0.0316032	+	0.219805i
$736$	6.36809			0.234731
$737$	−2.88363	+	20.0903i	−0.106220	+	0.740035i
$738$	4.33114			0.159432
$739$	−1.04531	+	7.27027i	−0.0384522	+	0.267441i	−0.999973	−	0.00728962i	$-0.997680\pi$
$739$	−1.04531	+	7.27027i	−0.0384522	+	0.267441i	0.961521	+	0.274731i	$0.0885887\pi$
$740$	2.85216	+	3.29157i	0.104848	+	0.121001i
$741$	6.15757	+	1.80802i	0.226204	+	0.0664194i
$742$	4.72516	+	3.03668i	0.173466	+	0.111480i
$743$	7.77966	−	4.99968i	0.285408	−	0.183421i	−0.390102	−	0.920772i	$-0.627560\pi$
$743$	7.77966	−	4.99968i	0.285408	−	0.183421i	0.675509	+	0.737351i	$0.263924\pi$
$744$	−0.280213	+	1.94892i	−0.0102731	+	0.0714510i
$745$	10.0364	−	21.9767i	0.367706	−	0.805163i
$746$	0.0145182	−	0.100977i	0.000531550	−	0.00369701i
$747$	3.54254	−	4.08831i	0.129615	−	0.149583i
$748$	14.1506	+	9.09403i	0.517397	+	0.332511i
$749$	4.02118	+	8.80516i	0.146931	+	0.321734i
$750$	−0.211618	−	0.463380i	−0.00772721	−	0.0169202i
$751$	−37.5811	−	11.0348i	−1.37136	−	0.402666i	−0.488604	−	0.872506i	$-0.662494\pi$
$751$	−37.5811	−	11.0348i	−1.37136	−	0.402666i	−0.882752	+	0.469840i	$0.844312\pi$
$752$	−0.635335	−	4.41885i	−0.0231683	−	0.161139i
$753$	4.87612	+	3.13369i	0.177696	+	0.114198i
$754$	22.9988	−	6.75306i	0.837567	−	0.245932i
$755$	11.6602	+	3.42373i	0.424357	+	0.124602i
$756$	1.80535	+	12.5565i	0.0656598	+	0.456674i
$757$	31.5793	+	36.4445i	1.14777	+	1.32460i	0.937915	+	0.346864i	$0.112754\pi$
$757$	31.5793	+	36.4445i	1.14777	+	1.32460i	0.209854	+	0.977733i	$0.432701\pi$
$758$	−28.8180	+	18.5202i	−1.04672	+	0.672685i
$759$	−5.26752	+	6.07904i	−0.191199	+	0.220655i
$760$	−2.89811	−	3.34460i	−0.105125	−	0.121321i
$761$	−28.0439	+	8.23444i	−1.01659	+	0.298498i	−0.747248	−	0.664546i	$-0.768625\pi$
$761$	−28.0439	+	8.23444i	−1.01659	+	0.298498i	−0.269344	+	0.963044i	$0.586807\pi$
$762$	1.61362	+	3.53332i	0.0584551	+	0.127999i
$763$	−28.9063	+	8.48767i	−1.04648	+	0.307274i
$764$	1.14329	−	0.734748i	0.0413628	−	0.0265823i
$765$	7.72294	−	16.9109i	0.279223	−	0.611414i
$766$	−7.45649			−0.269414
$767$	7.43084			0.268312
$768$	0.211618	−	0.463380i	0.00763612	−	0.0167208i
$769$	−6.74782	+	7.78740i	−0.243333	+	0.280821i	−0.864258	−	0.503049i	$-0.832212\pi$
$769$	−6.74782	+	7.78740i	−0.243333	+	0.280821i	0.620925	+	0.783870i	$0.286757\pi$
$770$	−1.53079	−	10.6469i	−0.0551660	−	0.383688i
$771$	−0.571325	−	3.97365i	−0.0205758	−	0.143108i
$772$	3.48096	−	4.01724i	0.125283	−	0.144584i
$773$	8.79389	−	19.2559i	0.316294	−	0.692588i	−0.682989	−	0.730428i	$-0.739320\pi$
$773$	8.79389	−	19.2559i	0.316294	−	0.692588i	0.999284	+	0.0378401i	$0.0120478\pi$
$774$	−30.6994			−1.10347
$775$	−3.86515			−0.138840
$776$	6.24819	−	13.6816i	0.224297	−	0.491142i
$777$	−8.09679	+	5.20349i	−0.290471	+	0.186674i
$778$	−13.3906	+	3.93185i	−0.480078	+	0.140964i
$779$	−2.90550	−	6.36216i	−0.104100	−	0.227948i
$780$	−1.39137	+	0.408544i	−0.0498191	+	0.0146282i
$781$	14.3986	+	16.6169i	0.515222	+	0.594598i
$782$	28.2898	−	32.6481i	1.01164	−	1.16749i
$783$	−20.7148	+	13.3126i	−0.740287	+	0.475753i
$784$	−7.73931	−	8.93164i	−0.276404	−	0.318987i
$785$	0.663278	+	4.61320i	0.0236734	+	0.164652i
$786$	5.54256	+	1.62744i	0.197697	+	0.0580490i
$787$	−14.2939	+	4.19705i	−0.509521	+	0.149609i	−0.526381	−	0.850249i	$-0.676451\pi$
$787$	−14.2939	+	4.19705i	−0.509521	+	0.149609i	0.0168598	+	0.999858i	$0.494633\pi$
$788$	−9.07200	−	5.83022i	−0.323176	−	0.207693i
$789$	0.140794	+	0.979244i	0.00501240	+	0.0348620i
$790$	15.8147	+	4.64360i	0.562660	+	0.165212i
$791$	32.3650	+	70.8694i	1.15077	+	2.51983i
$792$	−2.82285	−	6.18119i	−0.100306	−	0.219639i
$793$	−3.64867	−	2.34486i	−0.129568	−	0.0832684i
$794$	−25.5983	+	29.5420i	−0.908448	+	1.04841i
$795$	0.0938689	−	0.652872i	0.00332919	−	0.0231550i
$796$	3.58437	−	7.84868i	0.127045	−	0.278189i
$797$	7.34381	−	51.0773i	0.260131	−	1.80925i	−0.271680	−	0.962388i	$-0.587579\pi$
$797$	7.34381	−	51.0773i	0.260131	−	1.80925i	0.531811	−	0.846863i	$-0.321512\pi$
$798$	8.22723	−	5.28732i	0.291241	−	0.187169i
$799$	−25.4771	−	16.3731i	−0.901315	−	0.579240i
$800$	0.959493	+	0.281733i	0.0339232	+	0.00996075i
$801$	30.1861	+	34.8367i	1.06657	+	1.23089i
$802$	3.93864	−	27.3939i	0.139078	−	0.967311i
$803$	−14.0580			−0.496095
$804$	2.72984	−	3.15193i	0.0962740	−	0.111160i
$805$	−27.6248			−0.973646
$806$	−1.56584	+	10.8906i	−0.0551543	+	0.383607i
$807$	4.17580	+	4.81913i	0.146995	+	0.169641i
$808$	−6.83520	−	2.00699i	−0.240461	−	0.0706058i
$809$	−0.809114	−	0.519986i	−0.0284469	−	0.0182817i	0.526340	−	0.850274i	$-0.323564\pi$
$809$	−0.809114	−	0.519986i	−0.0284469	−	0.0182817i	−0.554787	+	0.831992i	$0.687200\pi$
$810$	−5.66316	+	3.63949i	−0.198983	+	0.127879i
$811$	−1.57389	+	10.9466i	−0.0552667	+	0.384388i	0.943350	+	0.331800i	$0.107656\pi$
$811$	−1.57389	+	10.9466i	−0.0552667	+	0.384388i	−0.998616	+	0.0525879i	$0.983253\pi$
$812$	15.1742	−	33.2268i	0.532509	−	1.16603i
$813$	−0.279375	+	1.94309i	−0.00979809	+	0.0681472i
$814$	7.07214	−	8.16169i	0.247879	−	0.286067i
$815$	−1.11257	−	0.715003i	−0.0389715	−	0.0250454i
$816$	−1.43557	−	3.14346i	−0.0502550	−	0.110043i
$817$	20.5944	+	45.0954i	0.720506	+	1.57769i
$818$	4.14109	+	1.21593i	0.144790	+	0.0425141i
$819$	4.81614	+	33.4970i	0.168290	+	1.17048i
$820$	1.32954	+	0.854441i	0.0464294	+	0.0298384i
$821$	−28.0783	+	8.24452i	−0.979938	+	0.287736i	−0.732199	−	0.681091i	$-0.761506\pi$
$821$	−28.0783	+	8.24452i	−0.979938	+	0.287736i	−0.247739	+	0.968827i	$0.579688\pi$
$822$	−0.431041	−	0.126565i	−0.0150343	−	0.00441447i
$823$	−5.80544	−	40.3777i	−0.202365	−	1.40748i	−0.797241	−	0.603661i	$-0.793708\pi$
$823$	−5.80544	−	40.3777i	−0.202365	−	1.40748i	0.594876	−	0.803817i	$-0.297201\pi$
$824$	−3.73420	−	4.30950i	−0.130087	−	0.150128i
$825$	−1.06261	+	0.682899i	−0.0369954	+	0.0237755i
$826$	7.41560	−	8.55806i	0.258022	−	0.297773i
$827$	9.78918	+	11.2973i	0.340403	+	0.392846i	0.899979	−	0.435933i	$-0.143581\pi$
$827$	9.78918	+	11.2973i	0.340403	+	0.392846i	−0.559576	+	0.828779i	$0.689036\pi$
$828$	−16.7448	+	4.91672i	−0.581923	+	0.170868i
$829$	6.99494	+	15.3168i	0.242944	+	0.531974i	0.991346	−	0.131271i	$-0.0419059\pi$
$829$	6.99494	+	15.3168i	0.242944	+	0.531974i	−0.748402	+	0.663245i	$0.769179\pi$
$830$	1.89399	−	0.556126i	0.0657414	−	0.0193034i
$831$	−7.57771	+	4.86990i	−0.262868	+	0.168935i
$832$	1.18253	−	2.58938i	0.0409969	−	0.0897706i
$833$	−80.1723			−2.77780
$834$	6.92814			0.239902
$835$	−5.60479	+	12.2728i	−0.193962	+	0.424717i
$836$	−7.18607	+	8.29317i	−0.248535	+	0.286825i
$837$	−1.60856	−	11.1878i	−0.0556000	−	0.386706i
$838$	−5.72297	−	39.8042i	−0.197697	−	1.37501i
$839$	−18.7493	+	21.6378i	−0.647297	+	0.747021i	−0.980647	−	0.195782i	$-0.937275\pi$
$839$	−18.7493	+	21.6378i	−0.647297	+	0.747021i	0.333350	+	0.942803i	$0.391821\pi$
$840$	−0.918001	+	2.01014i	−0.0316740	+	0.0693564i
$841$	41.9033			1.44494
$842$	−22.2546			−0.766944
$843$	−6.35619	+	13.9181i	−0.218919	+	0.479365i
$844$	2.09583	−	1.34691i	0.0721413	−	0.0463624i
$845$	4.69837	−	1.37957i	0.161629	−	0.0474586i
$846$	5.08234	+	11.1288i	0.174734	+	0.382615i
$847$	20.1942	−	5.92956i	0.693882	−	0.203742i
$848$	0.847909	+	0.978539i	0.0291173	+	0.0336032i
$849$	−9.44290	+	10.8977i	−0.324080	+	0.374008i
$850$	5.70687	−	3.66758i	0.195744	−	0.125797i
$851$	−18.1628	−	20.9610i	−0.622614	−	0.718535i
$852$	−0.642859	−	4.47118i	−0.0220240	−	0.153180i
$853$	22.6828	+	6.66027i	0.776644	+	0.228043i	0.645950	−	0.763379i	$-0.276461\pi$
$853$	22.6828	+	6.66027i	0.776644	+	0.228043i	0.130694	+	0.991423i	$0.458280\pi$
$854$	−6.34175	+	1.86211i	−0.217010	+	0.0637199i
$855$	10.2029	+	6.55698i	0.348931	+	0.224244i
$856$	0.317565	+	2.20871i	0.0108541	+	0.0754922i
$857$	28.8972	+	8.48499i	0.987110	+	0.289842i	0.735156	−	0.677898i	$-0.237109\pi$
$857$	28.8972	+	8.48499i	0.987110	+	0.289842i	0.251954	+	0.967739i	$0.418927\pi$
$858$	1.49369	+	3.27072i	0.0509937	+	0.111661i
$859$	6.72399	+	14.7235i	0.229420	+	0.502359i	0.988975	−	0.148084i	$-0.0473106\pi$
$859$	6.72399	+	14.7235i	0.229420	+	0.502359i	−0.759555	+	0.650443i	$0.774583\pi$
$860$	−9.42382	−	6.05632i	−0.321350	−	0.206519i
$861$	−2.28709	+	2.63944i	−0.0779438	+	0.0899519i
$862$	−2.08496	+	14.5012i	−0.0710139	+	0.493912i
$863$	14.9137	−	32.6564i	0.507667	−	1.11164i	−0.466233	−	0.884662i	$-0.654389\pi$
$863$	14.9137	−	32.6564i	0.507667	−	1.11164i	0.973901	−	0.226975i	$-0.0728834\pi$
$864$	−0.416170	+	2.89453i	−0.0141584	+	0.0984738i
$865$	−14.7494	+	9.47886i	−0.501494	+	0.322291i
$866$	3.19627	+	2.05412i	0.108614	+	0.0698018i
$867$	−14.1841	−	4.16484i	−0.481719	−	0.141445i
$868$	10.9801	+	12.6717i	0.372688	+	0.430105i
$869$	5.81627	−	40.4531i	0.197304	−	1.37228i
$870$	−4.28948			−0.145427
$871$	15.2544	−	17.6131i	0.516877	−	0.596797i
$872$	−6.94483			−0.235182
$873$	−5.86613	+	40.7998i	−0.198538	+	1.38086i
$874$	18.4554	+	21.2987i	0.624264	+	0.720439i
$875$	−4.16228	−	1.22216i	−0.140711	−	0.0413164i
$876$	2.42965	+	1.56144i	0.0820902	+	0.0527562i
$877$	24.7092	−	15.8796i	0.834370	−	0.536217i	−0.0522938	−	0.998632i	$-0.516653\pi$
$877$	24.7092	−	15.8796i	0.834370	−	0.536217i	0.886664	+	0.462415i	$0.153017\pi$
$878$	−5.26178	+	36.5965i	−0.177577	+	1.23507i
$879$	−2.62109	+	5.73939i	−0.0884073	+	0.193585i
$880$	0.352880	−	2.45433i	0.0118956	−	0.0827356i
$881$	−3.03996	+	3.50830i	−0.102419	+	0.118198i	−0.804645	−	0.593757i	$-0.797644\pi$
$881$	−3.03996	+	3.50830i	−0.102419	+	0.118198i	0.702226	+	0.711954i	$0.252190\pi$
$882$	27.2464	+	17.5102i	0.917435	+	0.589600i
$883$	−0.616939	−	1.35091i	−0.0207616	−	0.0454617i	0.898967	−	0.438016i	$-0.144319\pi$
$883$	−0.616939	−	1.35091i	−0.0207616	−	0.0454617i	−0.919729	+	0.392554i	$0.871591\pi$
$884$	−8.02201	−	17.5658i	−0.269810	−	0.590800i
$885$	−1.27591	−	0.374641i	−0.0428893	−	0.0125934i
$886$	−3.06817	−	21.3396i	−0.103077	−	0.716917i
$887$	42.8774	+	27.5556i	1.43968	+	0.925228i	0.999628	+	0.0272565i	$0.00867710\pi$
$887$	42.8774	+	27.5556i	1.43968	+	0.925228i	0.440054	+	0.897971i	$0.354959\pi$
$888$	−2.12882	+	0.625077i	−0.0714384	+	0.0209762i
$889$	31.7379	+	9.31909i	1.06445	+	0.312552i
$890$	2.39375	+	16.6489i	0.0802388	+	0.558073i
$891$	10.9309	+	12.6150i	0.366201	+	0.422618i
$892$	−3.73716	+	2.40173i	−0.125129	+	0.0804158i
$893$	12.9380	−	14.9312i	0.432954	−	0.499655i
$894$	8.05966	+	9.30134i	0.269555	+	0.311083i
$895$	13.2915	−	3.90273i	0.444285	−	0.130454i
$896$	−1.80207	−	3.94598i	−0.0602030	−	0.131826i
$897$	8.86038	−	2.60164i	0.295840	−	0.0868663i
$898$	13.7123	−	8.81235i	0.457585	−	0.294072i
$899$	−13.5202	+	29.6050i	−0.450923	+	0.987383i
$900$	−2.74050			−0.0913499
$901$	8.78357			0.292623
$902$	1.62792	−	3.56464i	0.0542037	−	0.118690i
$903$	16.2110	−	18.7085i	0.539469	−	0.622580i
$904$	2.55596	+	17.7771i	0.0850099	+	0.591257i
$905$	−1.70453	−	11.8553i	−0.0566604	−	0.394082i
$906$	−4.05399	+	4.67856i	−0.134685	+	0.155435i
$907$	13.1501	−	28.7948i	0.436643	−	0.956116i	−0.555559	−	0.831477i	$-0.687496\pi$
$907$	13.1501	−	28.7948i	0.436643	−	0.956116i	0.992202	−	0.124639i	$-0.0397771\pi$
$908$	15.0237			0.498581
$909$	19.5226			0.647525
$910$	−5.12982	+	11.2327i	−0.170052	+	0.372362i
$911$	42.3282	−	27.2027i	1.40240	−	0.901265i	0.402497	−	0.915421i	$-0.368143\pi$
$911$	42.3282	−	27.2027i	1.40240	−	0.901265i	0.999900	+	0.0141560i	$0.00450614\pi$
$912$	2.16311	−	0.635147i	0.0716278	−	0.0210318i
$913$	−2.03327	−	4.45224i	−0.0672914	−	0.147348i
$914$	15.8735	−	4.66087i	0.525048	−	0.154168i
$915$	0.508274	+	0.586579i	0.0168030	+	0.0193917i
$916$	−13.2467	+	15.2875i	−0.437684	+	0.505115i
$917$	41.3823	−	26.5948i	1.36656	−	0.878237i
$918$	12.9909	+	14.9923i	0.428765	+	0.494821i
$919$	1.82404	+	12.6865i	0.0601696	+	0.418489i	0.997537	+	0.0701457i	$0.0223464\pi$
$919$	1.82404	+	12.6865i	0.0601696	+	0.418489i	−0.937367	+	0.348343i	$0.886744\pi$
$920$	−6.11014	−	1.79410i	−0.201445	−	0.0591497i
$921$	−13.7116	+	4.02608i	−0.451812	+	0.132664i
$922$	−16.5905	−	10.6621i	−0.546379	−	0.351137i
$923$	−3.59232	−	24.9851i	−0.118243	−	0.822395i
$924$	5.25750	+	1.54374i	0.172959	+	0.0507854i
$925$	−1.80929	−	3.96179i	−0.0594890	−	0.130263i
$926$	14.2445	+	31.1911i	0.468103	+	1.02500i
$927$	13.1463	+	8.44864i	0.431783	+	0.277490i
$928$	5.51420	−	6.36372i	0.181012	−	0.208899i
$929$	−2.76531	+	19.2332i	−0.0907269	+	0.631020i	0.892826	+	0.450401i	$0.148719\pi$
$929$	−2.76531	+	19.2332i	−0.0907269	+	0.631020i	−0.983553	+	0.180619i	$0.942190\pi$
$930$	0.817937	−	1.79103i	0.0268212	−	0.0587303i
$931$	7.44336	−	51.7697i	0.243946	−	1.69668i
$932$	6.29642	−	4.04647i	0.206246	−	0.132546i
$933$	1.81315	+	1.16524i	0.0593597	+	0.0381482i
$934$	2.61594	+	0.768110i	0.0855962	+	0.0251333i
$935$	−11.0153	−	12.7123i	−0.360239	−	0.415738i
$936$	−1.11022	+	7.72176i	−0.0362887	+	0.252394i
$937$	−38.1576			−1.24656			−0.623278	−	0.782000i	$-0.714200\pi$
$937$	−38.1576			−1.24656			−0.623278	+	0.782000i	$0.714200\pi$
$938$	−5.06175	−	35.1454i	−0.165272	−	1.14754i
$939$	−10.0190			−0.326958
$940$	−0.635335	+	4.41885i	−0.0207223	+	0.144127i
$941$	16.9202	+	19.5270i	0.551584	+	0.636562i	0.961252	−	0.275673i	$-0.0889006\pi$
$941$	16.9202	+	19.5270i	0.551584	+	0.636562i	−0.409667	+	0.912235i	$0.634355\pi$
$942$	−2.27802	−	0.668888i	−0.0742221	−	0.0217936i
$943$	−8.46661	−	5.44116i	−0.275711	−	0.177188i
$944$	2.19601	−	1.41129i	0.0714741	−	0.0459336i
$945$	1.80535	−	12.5565i	0.0587279	−	0.408462i
$946$	−11.5388	+	25.2664i	−0.375158	+	0.821480i
$947$	4.22394	−	29.3782i	0.137260	−	0.954662i	−0.798493	−	0.602004i	$-0.794369\pi$
$947$	4.22394	−	29.3782i	0.137260	−	0.954662i	0.935752	−	0.352658i	$-0.114722\pi$
$948$	−5.49842	+	6.34552i	−0.178580	+	0.206093i
$949$	13.5770	+	8.72539i	0.440727	+	0.283238i
$950$	1.83843	+	4.02561i	0.0596467	+	0.130608i
$951$	−3.47509	−	7.60938i	−0.112687	−	0.246751i
$952$	−28.2360	−	8.29082i	−0.915132	−	0.268707i
$953$	−5.99544	−	41.6992i	−0.194211	−	1.35077i	−0.820709	−	0.571347i	$-0.806421\pi$
$953$	−5.99544	−	41.6992i	−0.194211	−	1.35077i	0.626497	−	0.779424i	$-0.284488\pi$
$954$	−2.98508	−	1.91840i	−0.0966456	−	0.0621104i
$955$	−1.30398	+	0.382884i	−0.0421959	+	0.0123898i
$956$	−13.5169	−	3.96891i	−0.437166	−	0.128364i
$957$	1.51367	+	10.5278i	0.0489300	+	0.340316i
$958$	−13.1941	−	15.2268i	−0.426281	−	0.491954i
$959$	−3.21827	+	2.06826i	−0.103923	+	0.0667875i
$960$	−0.333595	+	0.384990i	−0.0107667	+	0.0124255i
$961$	10.5175	+	12.1378i	0.339273	+	0.391542i
$962$	−11.8959	+	3.49295i	−0.383539	+	0.112617i
$963$	−2.54035	−	5.56259i	−0.0818616	−	0.179252i
$964$	0.219822	−	0.0645456i	0.00707999	−	0.00207887i
$965$	−4.47175	+	2.87382i	−0.143951	+	0.0925114i
$966$	5.84591	−	12.8008i	0.188089	−	0.411858i
$967$	−24.2019			−0.778279			−0.389140	−	0.921179i	$-0.627228\pi$
$967$	−24.2019			−0.778279			−0.389140	+	0.921179i	$0.627228\pi$
$968$	4.85172			0.155940
$969$	6.35317	−	13.9115i	0.204093	−	0.446902i
$970$	−9.84965	+	11.3671i	−0.316253	+	0.364976i
$971$	−4.19065	−	29.1466i	−0.134484	−	0.935359i	−0.939608	−	0.342252i	$-0.888810\pi$
$971$	−4.19065	−	29.1466i	−0.134484	−	0.935359i	0.805124	−	0.593107i	$-0.202099\pi$
$972$	−1.73655	−	12.0780i	−0.0556998	−	0.387401i
$973$	38.6353	−	44.5875i	1.23859	−	1.42941i
$974$	−10.5867	+	23.1816i	−0.339219	+	0.742786i
$975$	1.45011			0.0464407
$976$	−1.52362			−0.0487700
$977$	−7.66000	+	16.7731i	−0.245065	+	0.536618i	−0.991693	−	0.128624i	$-0.958944\pi$
$977$	−7.66000	+	16.7731i	−0.245065	+	0.536618i	0.746628	+	0.665241i	$0.231671\pi$
$978$	0.566757	−	0.364233i	0.0181229	−	0.0116469i
$979$	40.0173	−	11.7501i	1.27896	−	0.375536i
$980$	4.90948	+	10.7503i	0.156828	+	0.343404i
$981$	18.2613	−	5.36201i	0.583040	−	0.171196i
$982$	12.8161	+	14.7905i	0.408977	+	0.471984i
$983$	1.12501	−	1.29833i	0.0358822	−	0.0414103i	−0.737525	−	0.675320i	$-0.764006\pi$
$983$	1.12501	−	1.29833i	0.0358822	−	0.0414103i	0.773407	+	0.633910i	$0.218551\pi$
$984$	−0.677285	+	0.435264i	−0.0215910	+	0.0138757i
$985$	7.06195	+	8.14993i	0.225013	+	0.259678i
$986$	−8.12932	−	56.5407i	−0.258890	−	1.80062i
$987$	−9.46575	−	2.77939i	−0.301298	−	0.0884691i
$988$	12.0875	−	3.54922i	0.384556	−	0.112916i
$989$	60.0118	+	38.5672i	1.90826	+	1.22637i
$990$	0.967066	+	6.72609i	0.0307354	+	0.213769i
$991$	−26.6738	−	7.83214i	−0.847321	−	0.248796i	−0.170879	−	0.985292i	$-0.554661\pi$
$991$	−26.6738	−	7.83214i	−0.847321	−	0.248796i	−0.676442	+	0.736496i	$0.736479\pi$
$992$	1.60564	+	3.51587i	0.0509792	+	0.111629i
$993$	2.22822	+	4.87913i	0.0707105	+	0.154835i
$994$	−32.3602	−	20.7966i	−1.02640	−	0.659629i
$995$	−5.65040	+	6.52091i	−0.179130	+	0.206727i
$996$	−0.143106	+	0.995323i	−0.00453448	+	0.0315380i
$997$	3.44976	−	7.55393i	0.109255	−	0.239235i	−0.847105	−	0.531425i	$-0.821657\pi$
$997$	3.44976	−	7.55393i	0.109255	−	0.239235i	0.956360	+	0.292190i	$0.0943839\pi$
$998$	−1.16469	+	8.10058i	−0.0368675	+	0.256419i
$999$	10.7145	−	6.88581i	0.338993	−	0.217857i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	670.2.k.c.461.3	✓	50
67.25	even	11	inner	670.2.k.c.561.3	yes	50

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
670.2.k.c.461.3	✓	50	1.1	even	1	trivial
670.2.k.c.561.3	yes	50	67.25	even	11	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

Level:	\( N \)	\(=\)	\( 670 = 2 \cdot 5 \cdot 67 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	670.k (of order \(11\), degree \(10\), minimal)

\(f(q)\)	\(=\)	\(q+(0.142315 - 0.989821i) q^{2} +(-0.333595 - 0.384990i) q^{3} +(-0.959493 - 0.281733i) q^{4} +(0.841254 + 0.540641i) q^{5} +(-0.428547 + 0.275410i) q^{6} +(-0.617362 + 4.29385i) q^{7} +(-0.415415 + 0.909632i) q^{8} +(0.390013 - 2.71260i) q^{9} +O(q^{10})\)	\(q+(0.142315 - 0.989821i) q^{2} +(-0.333595 - 0.384990i) q^{3} +(-0.959493 - 0.281733i) q^{4} +(0.841254 + 0.540641i) q^{5} +(-0.428547 + 0.275410i) q^{6} +(-0.617362 + 4.29385i) q^{7} +(-0.415415 + 0.909632i) q^{8} +(0.390013 - 2.71260i) q^{9} +(0.654861 - 0.755750i) q^{10} +(-2.08595 - 1.34056i) q^{11} +(0.211618 + 0.463380i) q^{12} +(1.18253 + 2.58938i) q^{13} +(4.16228 + 1.22216i) q^{14} +(-0.0724972 - 0.504229i) q^{15} +(0.841254 + 0.540641i) q^{16} +(6.50898 - 1.91121i) q^{17} +(-2.62949 - 0.772087i) q^{18} +(0.629819 + 4.38049i) q^{19} +(-0.654861 - 0.755750i) q^{20} +(1.85904 - 1.19473i) q^{21} +(-1.62377 + 1.87394i) q^{22} +(4.17021 + 4.81268i) q^{23} +(0.488779 - 0.143519i) q^{24} +(0.415415 + 0.909632i) q^{25} +(2.73132 - 0.801987i) q^{26} +(-2.46007 + 1.58099i) q^{27} +(1.80207 - 3.94598i) q^{28} +8.42041 q^{29} -0.509414 q^{30} +(-1.60564 + 3.51587i) q^{31} +(0.654861 - 0.755750i) q^{32} +(0.179762 + 1.25027i) q^{33} +(-0.965431 - 6.71472i) q^{34} +(-2.84079 + 3.27844i) q^{35} +(-1.13844 + 2.49284i) q^{36} -4.35537 q^{37} +4.42554 q^{38} +(0.602398 - 1.31907i) q^{39} +(-0.841254 + 0.540641i) q^{40} +(-1.51640 + 0.445257i) q^{41} +(-0.918001 - 2.01014i) q^{42} +(10.7484 - 3.15600i) q^{43} +(1.62377 + 1.87394i) q^{44} +(1.79464 - 2.07113i) q^{45} +(5.35718 - 3.44285i) q^{46} +(-2.92349 - 3.37388i) q^{47} +(-0.0724972 - 0.504229i) q^{48} +(-11.3395 - 3.32959i) q^{49} +(0.959493 - 0.281733i) q^{50} +(-2.90716 - 1.86832i) q^{51} +(-0.405117 - 2.81765i) q^{52} +(1.24234 + 0.364785i) q^{53} +(1.21479 + 2.66003i) q^{54} +(-1.03005 - 2.25550i) q^{55} +(-3.64936 - 2.34530i) q^{56} +(1.47634 - 1.70379i) q^{57} +(1.19835 - 8.33470i) q^{58} +(1.08440 - 2.37451i) q^{59} +(-0.0724972 + 0.504229i) q^{60} +(-1.28175 + 0.823733i) q^{61} +(3.25157 + 2.08966i) q^{62} +(11.4067 + 3.34932i) q^{63} +(-0.654861 - 0.755750i) q^{64} +(-0.405117 + 2.81765i) q^{65} +1.26313 q^{66} +(-3.40210 - 7.44484i) q^{67} -6.78377 q^{68} +(0.461669 - 3.21098i) q^{69} +(2.84079 + 3.27844i) q^{70} +(-8.50817 - 2.49822i) q^{71} +(2.30545 + 1.48162i) q^{72} +(4.76950 - 3.06517i) q^{73} +(-0.619834 + 4.31104i) q^{74} +(0.211618 - 0.463380i) q^{75} +(0.629819 - 4.38049i) q^{76} +(7.04394 - 8.12913i) q^{77} +(-1.21991 - 0.783989i) q^{78} +(6.84700 + 14.9928i) q^{79} +(0.415415 + 0.909632i) q^{80} +(-6.45913 - 1.89657i) q^{81} +(0.224918 + 1.56434i) q^{82} +(1.66059 + 1.06720i) q^{83} +(-2.12033 + 0.622584i) q^{84} +(6.50898 + 1.91121i) q^{85} +(-1.59423 - 11.0881i) q^{86} +(-2.80901 - 3.24177i) q^{87} +(2.08595 - 1.34056i) q^{88} +(-11.0148 + 12.7118i) q^{89} +(-1.79464 - 2.07113i) q^{90} +(-11.8485 + 3.47902i) q^{91} +(-2.64540 - 5.79262i) q^{92} +(1.88921 - 0.554721i) q^{93} +(-3.75560 + 2.41358i) q^{94} +(-1.83843 + 4.02561i) q^{95} -0.509414 q^{96} -15.0408 q^{97} +(-4.90948 + 10.7503i) q^{98} +(-4.44995 + 5.13552i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 50 q + 5 q^{2} - 2 q^{3} - 5 q^{4} - 5 q^{5} + 2 q^{6} - q^{7} + 5 q^{8} - q^{9}+O(q^{10}) \) 50 * q + 5 * q^2 - 2 * q^3 - 5 * q^4 - 5 * q^5 + 2 * q^6 - q^7 + 5 * q^8 - q^9	\( 50 q + 5 q^{2} - 2 q^{3} - 5 q^{4} - 5 q^{5} + 2 q^{6} - q^{7} + 5 q^{8} - q^{9} + 5 q^{10} - 12 q^{11} - 2 q^{12} + 24 q^{13} + 23 q^{14} - 2 q^{15} - 5 q^{16} + 31 q^{17} + q^{18} + 4 q^{19} - 5 q^{20} + 12 q^{21} + q^{22} + 27 q^{23} - 9 q^{24} - 5 q^{25} - 2 q^{26} - 14 q^{27} + 10 q^{28} - 36 q^{29} + 2 q^{30} - 13 q^{31} + 5 q^{32} - 42 q^{33} + 2 q^{34} + 21 q^{35} - q^{36} - 50 q^{37} - 26 q^{38} - 31 q^{39} + 5 q^{40} - 10 q^{41} + 21 q^{42} + 16 q^{43} - q^{44} - q^{45} + 17 q^{46} - 13 q^{47} - 2 q^{48} - 40 q^{49} + 5 q^{50} - 19 q^{51} - 20 q^{52} - 5 q^{53} + 47 q^{54} + 10 q^{55} + 12 q^{56} - 90 q^{57} - 8 q^{58} - 20 q^{59} - 2 q^{60} + 12 q^{61} + 13 q^{62} - 15 q^{63} - 5 q^{64} - 20 q^{65} + 20 q^{66} - 21 q^{67} - 24 q^{68} + 77 q^{69} - 21 q^{70} + 24 q^{71} + 12 q^{72} - 68 q^{73} - 16 q^{74} - 2 q^{75} + 4 q^{76} + 7 q^{77} + 53 q^{78} - 26 q^{79} - 5 q^{80} - 21 q^{81} + 21 q^{82} - 10 q^{83} + 12 q^{84} + 31 q^{85} - 27 q^{86} + 61 q^{87} + 12 q^{88} + 51 q^{89} + q^{90} - 10 q^{91} - 6 q^{92} - 38 q^{93} - 9 q^{94} + 15 q^{95} + 2 q^{96} + 72 q^{97} - 37 q^{98} - 32 q^{99}+O(q^{100}) \) 50 * q + 5 * q^2 - 2 * q^3 - 5 * q^4 - 5 * q^5 + 2 * q^6 - q^7 + 5 * q^8 - q^9 + 5 * q^10 - 12 * q^11 - 2 * q^12 + 24 * q^13 + 23 * q^14 - 2 * q^15 - 5 * q^16 + 31 * q^17 + q^18 + 4 * q^19 - 5 * q^20 + 12 * q^21 + q^22 + 27 * q^23 - 9 * q^24 - 5 * q^25 - 2 * q^26 - 14 * q^27 + 10 * q^28 - 36 * q^29 + 2 * q^30 - 13 * q^31 + 5 * q^32 - 42 * q^33 + 2 * q^34 + 21 * q^35 - q^36 - 50 * q^37 - 26 * q^38 - 31 * q^39 + 5 * q^40 - 10 * q^41 + 21 * q^42 + 16 * q^43 - q^44 - q^45 + 17 * q^46 - 13 * q^47 - 2 * q^48 - 40 * q^49 + 5 * q^50 - 19 * q^51 - 20 * q^52 - 5 * q^53 + 47 * q^54 + 10 * q^55 + 12 * q^56 - 90 * q^57 - 8 * q^58 - 20 * q^59 - 2 * q^60 + 12 * q^61 + 13 * q^62 - 15 * q^63 - 5 * q^64 - 20 * q^65 + 20 * q^66 - 21 * q^67 - 24 * q^68 + 77 * q^69 - 21 * q^70 + 24 * q^71 + 12 * q^72 - 68 * q^73 - 16 * q^74 - 2 * q^75 + 4 * q^76 + 7 * q^77 + 53 * q^78 - 26 * q^79 - 5 * q^80 - 21 * q^81 + 21 * q^82 - 10 * q^83 + 12 * q^84 + 31 * q^85 - 27 * q^86 + 61 * q^87 + 12 * q^88 + 51 * q^89 + q^90 - 10 * q^91 - 6 * q^92 - 38 * q^93 - 9 * q^94 + 15 * q^95 + 2 * q^96 + 72 * q^97 - 37 * q^98 - 32 * q^99

Introduction

L-functions

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